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Forma Normal de Jordan

JSFH Uma matriz quadrada \303\251 semelhante tanto a uma matriz diagonal ou para uma matriz de Jordan, ou seja, uma matriz diagonal com uma mistura de 1s e 0s sobre a superdiagonal. As colunas da matriz de transi\303\247\303\243o para uma matriz diagonaliz\303\241vel s\303\243o os autovetores da matriz. A matriz quadrada n\303\243o diagonaliz\303\241vel n\303\243o tem autovetores linearmente independentes "suficientes" e \303\251 semelhante \303\240 sua matriz de Jordan atrav\303\251s de uma matriz de transi\303\247\303\243o composta por autovetores e autovetores generalizados. Selecionar os autovetores "corretos" e encontrar os autovetores generalizados exigem bastante cuidado. A teoria subjacente \303\240 estrutura de apoio a forma de Jordan, s\303\243o algumas das matem\303\241ticas mais abstratas encontradas no primeiro curso de \303\241lgebra linear. Na verdade, muitos dos principais textos de gradua\303\247\303\243o hoje simplesmente omitem essa discuss\303\243o. Este artigo do m\303\252s explora os c\303\241lculos em que a matriz de transi\303\247\303\243o para a forma de Jordan pode ser constru\303\255da, e assim fazendo, ilustra algumas das teorias subjacentes. JSFH

JSFH LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== QyQtSSV3aXRoRzYiNiNJLkxpbmVhckFsZ2VicmFHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiUhIiI= QyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJKWNvbWJpbmF0R0YlISIi LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH Tabela 1 apresenta a matriz LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== 7\303\2277, sua forma normal de Jordan LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e a matriz de transi\303\247\303\243o LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== para a transforma\303\247\303\243o de similaridade 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. A matriz de Jordan \303\251 uma matriz diagonal por blocos, com quatro blocos distintos de ordens 2\303\2272, 3\303\2273, 1\303\2271, 1\303\2271. Os autovalores de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== aparecem na diagonal principal de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=; o autovalor 2 tem multiplicidade alg\303\251brica 7, mas multiplicidade geom\303\251trica 4, o mesmo n\303\272mero que o n\303\272mero de blocos em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Cada bloco conta para um dos quatro vetores. Para determinar as colunas de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, primeiro \303\251 necess\303\241rio saber o tamanho dos blocos em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Assim, algo deve ser aprendido sobre a estrutura de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== antes que se possa encontrar a matriz de transi\303\247\303\243o LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== que converte LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. JSFH QyQ+SSJBRzYiLUknTWF0cml4R0YlNiMvSSQlaWRHRiUiKl92ImZXISIi

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

JSFH

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder QyQ+SSJQRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMvSSQlaWRHRiUiKnN3ImZXISIi

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

JSFH

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder QyQ+SSJKRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMvSSQlaWRHRiUiKiN6PGZXISIi

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder Tabela 1 A matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, sua matriz de transi\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, e sua forma normal de Jordan LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= JSFH

JSFH Um autovetor de uma matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 um vetor que permanece invari\303\241vel sob a multiplica\303\247\303\243o por LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. Em particular, \303\251 um vetor LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EieEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjQ= que satisfaz a equa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ4RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9LUkjbW9HRiQ2LVEiPUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlYtRiw2JVEnJiM5NTU7RidGOkZERjVGRA==, para um valor espec\303\255fico da constante LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy chamado de autovalor. Claramente, se LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtaUdGJDYlUScmIzk1NTtGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjcvJSZmZW5jZUdGNi8lKnNlcGFyYXRvckdRJXRydWVGJy8lKXN0cmV0Y2h5R0Y2LyUqc3ltbWV0cmljR0Y2LyUobGFyZ2VvcEdGNi8lLm1vdmFibGVsaW1pdHNHRjYvJSdhY2NlbnRHRjYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GMTYnUSJ4RicvJSVib2xkR0ZCRjQvRjhRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRllGN0Y3Rjc= \303\251 um autopar para LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, ent\303\243o assim \303\251 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, para qualquer m\303\272ltiplo escalar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Assim, um autovetor \303\251 realmente uma "autodire\303\247\303\243o", isto \303\251, uma dire\303\247\303\243o que permanece inalterada sob a multiplica\303\247\303\243o por LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. Se LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 uma matriz de transi\303\247\303\243o pelo qual LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 semelhante \303\240 sua forma de Jordan LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, ent\303\243o temos 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, ou LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjQVBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEjUEpGJ0YvRjJGOQ==. Os autovetores e autovetores generalizados de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEYvRjI=s\303\243o as colunas de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. Para ver o que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEYvRjI=faz para estas colunas, \303\251 suficiente comparar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTEYvRjI=ao produto LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEjUEpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=, conforme previsto na Tabela 2. NiRJIlBHNiItSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YkSSxUeXBlc2V0dGluZ0c2JEYoSShfc3lzbGliR0YkNiRGI0kiSkdGJA==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

NiQtSSdNYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy9JJCVpZEdGKCIqc3ciZlctRiQ2Iy9GKyIqN3oiZlc=

JSFH Tabela 2 As matrizes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEjUEpGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvRjNRJ25vcm1hbEYn JSFH A inspe\303\247\303\243o cuidadosa das matrizes na Tabela 2 revelaria que se 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, ent\303\243o 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 As colunas 1, 3, 6 e 7 da matriz de transi\303\247\303\243o LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== s\303\243o autovetores; colunas 2, 3 e 5 s\303\243o autovetores generalizados. Tabela 3 declara isso em termos da matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdWJHRiQ2JS1GLDYnUSJwRicvJSVib2xkR0YxL0YwRj0vRjNRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRlktRiM2JS1JI21uR0YkNiRRIjJGJ0Y5Ri9GMi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjc3Nzc3OGVtRicvRk5GY29GaG5GNUZPLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GaW8tRlA2JUZSLUYjNiUtRmluNiRRIjFGJ0Y5Ri9GMkZcb0Y5 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 Tabela 3 Autovetores e autovetores generalizados de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= O Autoespa\303\247o \303\251 gerado por quatro vetores 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. Os autovetores generalizados 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 s\303\243o "encadeados" aos autovetores. H\303\241 cadeias de comprimentos 2, 3, 1 e 1. Na base de cada cadeia est\303\241 um autovetor. Os membros remanescentes de uma cadeia s\303\243o autovetores generalizados. Para determinar a estrutura da forma de Jordan LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, \303\251 preciso saber o n\303\272mero de cadeia e o comprimento de cada cadeia. JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= A tabela 4 define a matriz 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, com o autovalor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy ajustado para ser igual a 2, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= sendo a matriz identidade. PkkiQ0c2IiwmSSJBR0YkIiIiLUkvSWRlbnRpdHlNYXRyaXhHRiQ2IyIiKCEiIw==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKk9cKWVX

Tabela 4 A matriz 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Para a matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=\303\227LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= = 7\303\2277, seja LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEnJiM5NTc7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIj1GJ0YyLyUmZmVuY2VHRjEvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGMS8lKnN5bW1ldHJpY0dGMS8lKGxhcmdlb3BHRjEvJS5tb3ZhYmxlbGltaXRzR0YxLyUnYWNjZW50R0YxLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGSS1JI21uR0YkNiRRIjdGJ0YyRjI= a multiplicidade alg\303\251brica do autovalor 2, e determine o inteiro 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. Seja LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== o menor inteiro LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== para qual o posto de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImtGJ0YyRjVGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9GNlEnbm9ybWFsRic= \303\251 igual a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy. O inteiro LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 chamado de \303\255ndice de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. Tabela 5 mostra que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjNGJ0Y5Rjk= para a matriz LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== na Tabela 4. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklUmFua0c2IjYjSSJDR0Yk

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IiIk

LUklUmFua0c2IjYjKiRJIkNHRiQiIiM=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IiIi

LUklUmFua0c2IjYjKiRJIkNHRiQiIiQ=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

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JSFH Tabela 5 O \303\255ndice de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 3 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= O \303\255ndice de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= tamb\303\251m pode ser encontrado a partir do polin\303\264mio m\303\255nimo para LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. O teorema de Cayley-Hamilton afirma que 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, o polin\303\264mio caracter\303\255stico de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, aniquila LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= (i.e., LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRIkFGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tRiw2I1EhRidGPQ== \303\251 a matriz nula). O polin\303\264mio m\303\255nimo \303\251 o polin\303\264mio de grau mais baixo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== para que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRIkFGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSI9RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZULUkjbW5HRiQ2JFEiMEYnRj1GPQ== . Os polin\303\264mios caracter\303\255stico e m\303\255nimo para LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== s\303\243o apresentados na Tabela 6. LUknZmFjdG9yRzYiNiMtSTlDaGFyYWN0ZXJpc3RpY1BvbHlub21pYWxHRiQ2JEkiQUdGJEknbGFtYmRhR0Yk

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

KiQsJkknbGFtYmRhRzYiIiIiISIjRiYiIig=

LUknZmFjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMtSTJNaW5pbWFsUG9seW5vbWlhbEdGJzYkSSJBR0YnSSdsYW1iZGFHRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

KiQsJkknbGFtYmRhRzYiIiIiISIjRiYiIiQ=

JSFH Tabela 6 Polin\303\264mios caracter\303\255stico e m\303\255nimo para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= JSFH No polin\303\264mio m\303\255nimo, o grau do fator contendo um autovalor particular LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUYvNiVRImpGJy9GM1EldHJ1ZUYnL0Y2USdpdGFsaWNGJ0Y9Rj8vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0Y1 d\303\241 o \303\255ndice da matriz 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. O \303\255ndice de 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 \303\251 o comprimento da cadeia mais longa. Antes que n\303\263s possamos fazer mais progressos em desconstruir a estrutura de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, precisamos da seguinte defini\303\247\303\243o. O posto de x, um membro em uma cadeia de autovetores generalizados, \303\251 o menor inteiro LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== para que 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. Assim, 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, mas 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 Defini\303\247\303\243o 1 Posto de um autovetor generalizado Em ess\303\252ncia, o membro encadeado x tem posto LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEic0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= se x est\303\241 no espa\303\247o nulo de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRInNGJ0YyRjVGMkY1LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy9GNlEnbm9ybWFsRic=, n\303\243o no espa\303\247o nulo de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNiVRInNGJ0YyRjUtSSNtb0dGJDYtUSgmbWludXM7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZFLyUpc3RyZXRjaHlHRkUvJSpzeW1tZXRyaWNHRkUvJShsYXJnZW9wR0ZFLyUubW92YWJsZWxpbWl0c0dGRS8lJ2FjY2VudEdGRS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlQtSSNtbkdGJDYkUSIxRidGQUYyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRkE=. Atribuindo uma classifica\303\247\303\243o para um membro de uma cadeia de autovetores generalizados \303\251 simplesmente uma forma de grava\303\247\303\243o em que o espa\303\247o nulo que o vetor se encontra. Encontrando os comprimentos das cadeias mais curtas do que os mais longos requerem os n\303\272meros 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 Tabela 7 fornece os valores de 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, para a matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= na Tabela 1. Desde que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R0Y9LUkjbW9HRiQ2LVEiPUYnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkgvJSlzdHJldGNoeUdGSC8lKnN5bW1ldHJpY0dGSC8lKGxhcmdlb3BHRkgvJS5tb3ZhYmxlbGltaXRzR0ZILyUnYWNjZW50R0ZILyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVy1GLzYlUSJJRidGMkY1Rj4=, a classe de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R0Y9Rj4= \303\251 7. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIj1GJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWUY1 LCYiIigiIiItSSVSYW5rRzYiNiNJIkNHRichIiI=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IiIl

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIj1GJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWUY1 LCYtSSVSYW5rRzYiNiNJIkNHRiUiIiItRiQ2IyokRiciIiMhIiI=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IiIj

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NjE7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIj1GJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWUY1 LCYtSSVSYW5rRzYiNiMqJEkiQ0dGJSIiIyIiIi1GJDYjKiRGKCIiJCEiIg==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

= print(); # input placeholder

IiIi

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Tabela 7 Determina\303\247a\303\265 de 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 Os dados na Tabela 7 indicam que h\303\241 quatro vetores de posto 1 (os quatro autovetores); dois vetores de posto 2, e um vetor de posto 3. Esses vetores est\303\243o arranjados em quatro cadeias, representado na Figura 1. 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 Figura 1 Sobreposi\303\247\303\243o em subespa\303\247os em LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEoJnJlYWxzO0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSSVtcm93R0YkNiQtSSNtbkdGJDYkUSI3RidGMkYyLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJw== induzida pela matriz LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== Os vetores LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EicEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1JI21uR0YkNiRRIjZGJy9GOVEnbm9ybWFsRicvRjZGNC9GOVEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZD e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EicEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1JI21uR0YkNiRRIjdGJy9GOVEnbm9ybWFsRicvRjZGNC9GOVEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZD s\303\243o autovetores e nenhuma cadeia de autovetores generalizados emana de um desses dois vetores. O vetor LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EicEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSVtcm93R0YkNiQtSSNtbkdGJDYkUSIxRicvRjZRJ25vcm1hbEYnRkEvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== \303\251 um autovetor, e \303\251 o in\303\255cio de uma cadeia de comprimento 2. Assim, o vetor LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EicEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSVtcm93R0YkNiQtSSNtbkdGJDYkUSIyRicvRjZRJ25vcm1hbEYnRkEvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== \303\251 o autovetor generalizado no final desta cadeia de comprimento 2. O vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EicEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1JI21uR0YkNiRRIjNGJy9GOVEnbm9ybWFsRicvRjZGNC9GOVEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZD \303\251 um autovetor, o in\303\255cio da cadeia de comprimento 3. O autovetor generalizado LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EicEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSVtcm93R0YkNiQtSSNtbkdGJDYkUSI0RicvRjZRJ25vcm1hbEYnRkEvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw== \303\251 o segundo membro desta cadeia, e o autovetor generalizado LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2J1EicEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1JI21uR0YkNiRRIjVGJy9GOVEnbm9ybWFsRicvRjZGNC9GOVEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0ZD \303\251 o fim da cadeia mais longa. O autoespa\303\247oLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMUYnRi9GLy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRi8= \303\251 o espa\303\247o nulo da matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. O subespa\303\247o LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn \303\251 o espa\303\247o nulo de LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRic=, mas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RJiZzdWI7RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZYLUYsNiVGLi1GIzYlLUY7NiRRIjJGJ0Y+RjJGNUZARj4=, ou seja, o autoespa\303\247o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ \303\251 um subespa\303\247o de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. Da mesma forma, 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 de modo que LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn \303\251 um subespa\303\247o de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. Neste exemplo, 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, todo o espa\303\247o, ent\303\243o n\303\263s temos 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. Tabela 3, portanto, pode ser expressada pelas equa\303\247\303\265es na Tabela 8. 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdWJHRiQ2JS1GLDYnUSJwRicvJSVib2xkR0YxL0YwRj0vRjNRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRlktRiM2JC1JI21uR0YkNiRRIjdGJ0Y5RjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORmNvLUZpbjYmRl5vRlVGWEZaRjk= Tabela 8 Cadeias de autovetores generalizados e a matriz 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 JSFH

JSFH O comprimento de cadeia para os autovetores generalizados nos diz qual LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1GLDYlUSJrRidGL0YyL0YzUSdub3JtYWxGJy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn selecionaremos o final da cadeia. Como pode ser visto na Tabela 8, se o autovetor generalizado no final da cadeia \303\251 conhecido, a cadeia completa pode ser calculada multiplicando-se sucessivamente por LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. Portanto, primeiro obtemos bases para os espa\303\247os nulo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImtGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn . JSFH Qyc+SSROUzFHNiItSShjb252ZXJ0RyUqcHJvdGVjdGVkRzYkLUkqTnVsbFNwYWNlR0YlNiNJIkNHRiVJJWxpc3RHRigiIiI+SSROUzJHRiUtRic2JC1GKzYjKiRGLSIiI0YuRi8+SSROUzNHRiUtRic2JC1GKzYjKiRGLSIiJEYu

NyYtJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2NvbHVtbkdGKTYjL0kkJWlkR0YpIiohb0B2KSktRiQ2Iy9GLiIqPz5fKCkpLUYkNiMvRi4iKmdAXygpKS1GJDYjL0YuIiorQ18oKSk=

NygtJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2NvbHVtbkdGKTYjL0kkJWlkR0YpIiprUVoqKSktRiQ2Iy9GLiIqL1RaKikpLUYkNiMvRi4iKldWWiopKS1GJDYjL0YuIiolZXUlKikpLUYkNiMvRi4iKkNbWiopKS1GJDYjL0YuIiprXVoqKSk=

NyktJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2NvbHVtbkdGKTYjL0kkJWlkR0YpIiovQFwqKSktRiQ2Iy9GLiIqV0JcKikpLUYkNiMvRi4iKiVlI1wqKSktRiQ2Iy9GLiIqQ0dcKikpLUYkNiMvRi4iKmtJXCopKS1GJDYjL0YuIiovTFwqKSktRiQ2Iy9GLiIqV05cKikp

O autoespa\303\247o LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjFGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn \303\251 gerado por quatro autovetores em LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEkTlMxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn. O espa\303\247o envolvendo LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn \303\251 gerado pelos seis vetores base em LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEkTlMyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn . Dever\303\255amos ter antecipado os sete vetores em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkTlMzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== desde que 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, ent\303\243o, o vetor mais geral em LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjNGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn ser\303\241 PkkiWEc2Ii1JJDwsPkdJKF9zeXNsaWJHRiQ2Iy1JJHNlcUclKnByb3RlY3RlZEc2JCZJInhHRiQ2I0kia0dGJC9GMDsiIiIiIig=

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqa09cKikp

A cadeia de comprimento 3 "acaba" com um autovetor generalizado de posto 3. Este vetor encontra-se em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GLzYjUSFGJ0Y+ de modo que 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, mas LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYvNidRIlhGJy8lJWJvbGRHRjQvRjNRJmZhbHNlRicvRjZRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRktGPg== n\303\243o deve ser o vetor zero. Claramente, 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, como vemos em LUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHNiRGJUkoX3N5c2xpYkdGKDYkKiRJIkNHRigiIiRJIlhHRig=

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqWy9eISop

Temos de assegurar que 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 para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EiWEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjcvRjZRJ25vcm1hbEYn ser um autovetor generalizado de classe 3. Consequentemente, n\303\263s calculamos PkkkcGhpRzYiLUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEksVHlwZXNldHRpbmdHNiRGKEkoX3N5c2xpYkdGJDYkKiRJIkNHRiQiIiNJIlhHRiQ=

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqb3heISop

O vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EnJiM5NjY7RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNy9GNlEnbm9ybWFsRic= ser\303\241 diferente de zero desde que MCZJJHBoaUc2IjYjIiIiIiIh

MCwwJkkieEc2IjYjIiIiISNFJkYlNiMiIiMhI0smRiU2IyIiJCIjUSZGJTYjIiIlISNUJkYlNiMiIiYiIzomRiU2IyIiJyIjQiZGJTYjIiIoISIoIiIh

Assumindo que este seja o caso, tomamos 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, que \303\251 PkkkUGhpRzYiLUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEksVHlwZXNldHRpbmdHNiRGKEkoX3N5c2xpYkdGJDYkSSJDR0YkSSJYR0Yk

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqRyg9MCop

como o membro da cadeia em LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn e 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 como o membro no autoespa\303\247o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. Desde que a condi\303\247\303\243o em (1) prevale\303\247a, temos portanto a cadeia de comprimento 3 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EmJnBoaTtGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y3LUkjbW9HRiQ2LVEiLEYnL0Y2USdub3JtYWxGJy8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiVRJiZQaGk7RidGMkY+RjotRiw2J1EiWEYnRi9GMkY1RjhGPg==. Uma maneira alternativa de procurar na condi\303\247\303\243o 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 \303\251 observar que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EiWEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjcvRjZRJ25vcm1hbEYn deve situar-se em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ mas n\303\243o em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. Isso significa que a componente de X que est\303\241 no complemento ortogonal de LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn n\303\243o deve ser zero. Assim, para projetar X em LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn, formamos a matriz de proje\303\247\303\243o 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, onde LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 uma matriz cuja colunas s\303\243o os vetores que geram LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn. QyU+SSJNRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJJE5TMkdGJSEiIj5JIlBHRiUtSTBkZWxheURvdFByb2R1Y3RHNiRGKS9JK21vZHVsZW5hbWVHRiVJLFR5cGVzZXR0aW5nR0YoNiQtRjE2JEYkKiQtRjE2JC1fSS5MaW5lYXJBbGdlYnJhR0YoSSpUcmFuc3Bvc2VHRiU2I0YkRiRGLUY8

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKkNFXSEqKQ==

A componente de X ortogonal \303\240 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ \303\251 ent\303\243o PkkiTEc2IiwmSSJYR0YkIiIiLUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEksVHlwZXNldHRpbmdHNiRGK0koX3N5c2xpYkdGJDYkSSJQR0YkRiYhIiI=

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqL1xdISop

A condi\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EiTEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSNtb0dGJDYtUSI9RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGUC1JI21uR0YkNiZRIjBGJ0YvRjVGOEY+ gera sete equa\303\247\303\265es homog\303\252neas, a partir do qual LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ pode ser eliminado, dando-lhe o valor LUkqZWxpbWluYXRlRzYiNiQtSSdFcXVhdGVHRiQ2JEkiTEdGJC1JK1plcm9WZWN0b3JHRiQ2IyIiKCZJInhHRiQ2IyIiIg==

NyQ8Iy8mSSJ4RzYiNiMiIiIsLiZGJjYjIiImIyIjOiIjRSZGJjYjIiIjIyEjOyIjOCZGJjYjIiIkIyIjPkY2JkYmNiMiIiUjISNURjAmRiY2IyIiJyMiI0JGMCZGJjYjIiIoIyEiKEYwPCI=

O vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EnJiM5NjY7RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNy9GNlEnbm9ybWFsRic= \303\251 diferente de zero dado que LUkoaXNvbGF0ZUc2IjYkLyZJJHBoaUdGJDYjIiIiIiIhJkkieEdGJEYp

LyZJInhHNiI2IyIiIiwuJkYkNiMiIiYjIiM6IiNFJkYkNiMiIiMjISM7IiM4JkYkNiMiIiQjIiM+RjQmRiQ2IyIiJSMhI1RGLiZGJDYjIiInIyIjQkYuJkYkNiMiIigjISIoRi4=

n\303\243o se mantenha. As condi\303\247\303\265es s\303\243o as mesmas!

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= A cadeia de comprimento 2 "termina" em um autovetor generalizado em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ que \303\251 distinto do vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EnJiM5MzQ7RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNy9GNlEnbm9ybWFsRic=. Para encontrar um vetor em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSJ+RidGPi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGSS8lKXN0cmV0Y2h5R0ZJLyUqc3ltbWV0cmljR0ZJLyUobGFyZ2VvcEdGSS8lLm1vdmFibGVsaW1pdHNHRkkvJSdhY2NlbnRHRkkvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZYRj4=que \303\251 distinto de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EmJlBoaTtGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y0, considere como candidatos os seis vetores base em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkTlMyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw==. N\303\263s testamos a classifica\303\247\303\243o de cada matriz cuja primeira coluna \303\251 LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EmJlBoaTtGJy8lJWJvbGRHUSV0cnVlRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y0 e cuja segunda coluna \303\251 um desses vetores de base. Se a classifica\303\247\303\243o de qualquer uma dessas matrizes \303\251 2, ent\303\243o o vetor de base correspondente \303\251 um candidato para o autovetor generalizado de classe 2 que termina \303\240 cadeia de comprimento 2. Os c\303\241lculos relevantes s\303\243o ent\303\243o QyQtSSRzZXFHJSpwcm90ZWN0ZWRHNiQtSSVSYW5rRzYiNiMtSSdNYXRyaXhHNiRGJUkoX3N5c2xpYkdGKTYjNyRJJFBoaUdGKSZJJE5TMkdGKTYjSSJrR0YpL0Y1OyIiIiIiJ0Y4

NigiIiNGI0YjRiNGI0Yj

Os postos das seis matrizes poss\303\255veis s\303\243o todos 2; qualquer um dos seis vetores de base em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEkTlMyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnL0YzUSdub3JtYWxGJw== podem ser selecionados. A \303\242ncora da cadeia \303\251 ent\303\243o o autovetor PkkkY2hpRzYiLUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEksVHlwZXNldHRpbmdHNiRGKEkoX3N5c2xpYkdGJDYkSSJDR0YkJkkkTlMyR0YkNiMiIiI=

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqS18jUSop

onde o vetor selecionado de LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn \303\251 PkknTGFtYmRhRzYiJkkkTlMyR0YkNiMiIiI=

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqa1FaKikp

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Agora temos cinco das sete colunas da matriz de transi\303\247\303\243o. As duas colunas restantes s\303\243o autovetores retirados do subespa\303\247o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. H\303\241 PkkiTkc2Ii1JKW51bWJjb21iR0YkNiQiIiUiIiM=

IiIn

maneiras de escolher dois vetores diferentes de um conjunto de quatro. As combina\303\247\303\265es expl\303\255citas s\303\243o PkkmcGFpcnNHNiItSSdjaG9vc2VHRiQ2JCIiJSIiIw==

Nyg3JCIiIiIiIzckRiQiIiQ3JEYkIiIlNyRGJUYnNyRGJUYpNyRGJ0Yp

Um m\303\251todo de for\303\247a bruta para escolher dois que saem de um conjunto linearmente independente de sete vetores para as colunas da matriz de transi\303\247\303\243o simplesmente testa a classifica\303\247\303\243o de cada poss\303\255vel matriz de transi\303\247\303\243o que pode ser constru\303\255da a partir dos cinco vetores que j\303\241 temos. A matriz de transi\303\247\303\243o resultante LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 a primeira como matriz cujo posto \303\251 7. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= QyQ/KEkia0c2IiIiIkYmSSJOR0YlSSV0cnVlRyUqcHJvdGVjdGVkR0MkPkkiVEdGJS1JJ01hdHJpeEc2JEYpSShfc3lzbGliR0YlNiM3KUkkY2hpR0YlSSdMYW1iZGFHRiVJJHBoaUdGJUkkUGhpR0YlSSJYR0YlJkkkTlMxR0YlNiMmJkkmcGFpcnNHRiU2I0YkNiNGJiZGOTYjJkY8NiMiIiNAJC8tSSVSYW5rR0YlNiNGLCIiKEMkLUkmcHJpbnRHRik2I0Y8WyEiIg==

NyQiIiMiIiQ=

Para verificar se a matriz de transi\303\247\303\243o LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== coloca LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em sua forma de Jordan, mostramos LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjQVRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEjVEpGJ0YvRjJGOQ== ao inv\303\251s de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlEtSSNtbkdGJDYkUSIxRidGPkYyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUYvNiVRI0FURidGMkY1LUY7Ni1RIj1GJ0Y+RkBGQ0ZFRkdGSUZLRk0vRlBRLDAuMjc3Nzc3OGVtRicvRlNGXG8tRi82JVEiSkYnRjJGNUY+. A matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 dif\303\255cil de inverter, pois cont\303\251m muitas indetermina\303\247\303\265es; o teste seguinte que mostra que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjQVRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSgmbWludXM7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkwtRiw2JVEjVEpGJ0YvRjJGOQ== \303\251 a matriz zero, \303\251 portanto mais eficiente. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUkpc2ltcGxpZnlHNiI2IywmLUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUdGJEksVHlwZXNldHRpbmdHNiRGKkkoX3N5c2xpYkdGJDYkSSJBR0YkSSJUR0YkIiIiLUYoNiRGMkkiSkdGJCEiIg==

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKkspW0AiKg==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= H\303\241 uma certa flexibilidade nas escolhas dos autovetores generalizados nas cadeias cujos membros formam as colunas da matriz de transi\303\247\303\243o. Como uma experi\303\252ncia, vamos come\303\247ar com a matriz de transi\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= PkkiUUc2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYlIiIoRis3Iy1JJHNlcUdGKDYkJkkicUdGJDYjSSJrR0YkL0YzOyIiIiIjXA==

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKl8qW0AiKg==

cuja totalidade dos 7 \303\227 7 = 49 membros s\303\243o indeterminados. Por for\303\247a bruta, configurar e resolver as equa\303\247\303\265es inerentes em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjQVFGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSI9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEjUUpGJ0YvRjJGOQ==. As equa\303\247\303\265es s\303\243o QyQ+SSNFUUc2Ii1JJ0VxdWF0ZUdJKF9zeXNsaWJHRiU2JC1JMGRlbGF5RG90UHJvZHVjdEc2JCUqcHJvdGVjdGVkRy9JK21vZHVsZW5hbWVHRiVJLFR5cGVzZXR0aW5nRzYkRi1GKDYkSSJBR0YlSSJRR0YlLUYrNiRGNEkiSkdGJSEiIg== A solu\303\247\303\243o \303\251 QyQ+SSRzb2xHNiItSSZzb2x2ZUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSNFUUdGJSIiIg==

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

Isso traz a matriz de transi\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= para a forma QyQ+SSNRUUc2Ii1JJWV2YWxHJSpwcm90ZWN0ZWRHNiRJIlFHRiVJJHNvbEdGJSEiIg== contendo as indetermina\303\247\303\265es PkkjTDFHNiItSShjb252ZXJ0RyUqcHJvdGVjdGVkRzYkLUknaW5kZXRzR0YnNiNJI1FRR0YkSSVsaXN0R0Yn

NzcmSSJxRzYiNiMiIzYmRiQ2IyIjOiZGJDYjIiM7JkYkNiMiIz0mRiQ2IyIjPiZGJDYjIiM/JkYkNiMiI0AmRiQ2IyIjQiZGJDYjIiNFJkYkNiMiI0YmRiQ2IyIjRyZGJDYjIiNJJkYkNiMiI0wmRiQ2IyIjTSZGJDYjIiNOJkYkNiMiI08mRiQ2IyIjUCZGJDYjIiNSJkYkNiMiI1MmRiQ2IyIjVCZGJDYjIiNV

cujo n\303\272mero \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklbm9wc0clKnByb3RlY3RlZEc2I0kjTDFHNiI=

IiNA

Isso representa uma quantidade consider\303\241vel de escolha como seleciona autovetores generalizados. Quanta flexibilidade \303\251 deixada em escolha desses 21 par\303\242metros? Vamos designar aleatoriamente os seguintes valores para essas 21 inc\303\263gnitas atrav\303\251s de PkkjTDJHNiItX0ksUmFuZG9tVG9vbHNHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiRJKUdlbmVyYXRlR0YkNiMtSSVsaXN0R0YpNiQtSShpbnRlZ2VyR0YpNiMvSSZyYW5nZUdGKTshIiIiIiIiI0A=

NzciIiEhIiJGI0YjIiIiRiVGJUYlRiVGJUYjRiVGJEYkRiNGI0YlRiRGI0YlRiM=

para essas 21 inc\303\263gnitas. A matriz de transi\303\247\303\243o resultante ser\303\241 ent\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= PkkiU0c2Ii1JJWV2YWxHJSpwcm90ZWN0ZWRHNiRJI1FRR0YkLUknRXF1YXRlR0koX3N5c2xpYkdGJDYkSSNMMUdGJEkjTDJHRiQ=

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKiN6Ij05Kg==

cuja classifica\303\247\303\243o verificamos com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= LUklUmFua0c2IjYjSSJTR0Yk

IiIn

e que n\303\263s testamos com LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= 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

Error, (in rtable/Power) singular matrix

Se a classifica\303\247\303\243o de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= n\303\243o \303\251 7, uma lista diferente LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ precisaria ser gerada.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Uma pergunta ainda mais interessante \303\251 se o processo de constru\303\247\303\243o de cadeias de autovetores generalizados pode ser revertido. Em outras palavras, podemos come\303\247ar com um autovetor E e ir adiante na cadeia por resolu\303\247\303\243o de equa\303\247\303\265es da forma LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUSJ1RicvRjBRJmZhbHNlRicvRjNRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiPUYnRjovJSZmZW5jZUdGOS8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZQLUYsNidRIkVGJy8lJWJvbGRHRjFGOC9GM1ElYm9sZEYnLyUrZm9udHdlaWdodEdGWUY6 para um autovetor generalizado u? Bem, a resposta \303\251 um sim qualificado, e os c\303\241lculos, apresentados abaixo, mostram como isso pode ser feito. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Para a equa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ1RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9LUkjbW9HRiQ2LVEiPUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlYtRiw2J1EiRUYnRjhGOkY8Rj5GRA== ter uma solu\303\247\303\243o, o vetor E tem que ser no espa\303\247o coluna de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. Assim, E deve estar no espa\303\247o nulo de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= porque \303\251 um autovetor, e tem que estar no espa\303\247o coluna de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== a fim de suportar uma cadeia de autovetores generalizados. Para encontrar uma base para o subespa\303\247o de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ que \303\251 comum para o espa\303\247o coluna de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, primeiro encontramos PkkjQ1NHNiItSSxDb2x1bW5TcGFjZUdGJDYjSSJDR0Yk

NyUtJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2NvbHVtbkdGKTYjL0kkJWlkR0YpIipfaj05Ki1GJDYjL0YuIipzaz05Ki1GJDYjL0YuIiojZic9OSo=

uma base para o espa\303\247o coluna de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, ent\303\243o utilize QyQ+SSNJQkc2Ii1JMkludGVyc2VjdGlvbkJhc2lzR0YlNiM3JEkkTlMxR0YlSSNDU0dGJSIiIg==

NyQtJkknVmVjdG9yRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ2NvbHVtbkdGKTYjL0kkJWlkR0YpIipfTj45Ki1GJDYjL0YuIipzTz45Kg==

para encontrar uma base para a interse\303\247\303\243o de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ com o espa\303\247o coluna de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Assim, o autovetor mais geral que pode suportar uma cadeia de autovetores generalizados \303\251 PkkiR0c2IiwmKiZJInVHRiQiIiImSSNJQkdGJDYjRihGKEYoKiZJInZHRiRGKCZGKjYjIiIjRihGKA==

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqX1Q+OSo=

A solu\303\247\303\243o mais geral da equa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ1RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9LUkjbW9HRiQ2LVEiPUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlYtRiw2J1EiR0YnRjhGOkY8Rj5GRA== \303\251 QyQ+SSJVRzYiLUksTGluZWFyU29sdmVHRiU2JUkiQ0dGJUkiR0dGJS9JJWZyZWVHRiVJInRHRiUiIiI=

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqX2A+OSo=

No entanto, a cadeia n\303\243o pode ser avan\303\247ada para um vetor em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ porque U n\303\243o \303\251 no espa\303\247o coluna de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. Os par\303\242metros livres em U mostram que cont\303\251m componentes a partir do espa\303\247o nulo de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. Mesmo que estes componentes n\303\243o estavam l\303\241, U ainda n\303\243o estaria no espa\303\247o coluna de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, como podemos verificar mostrando a componente de U ortogonal ao espa\303\247o coluna de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 diferente de zero. A matriz de proje\303\247\303\243o \303\251 QyU+SSJNRzYiLUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiNJI0NTR0YlISIiPkkiUEdGJS1JMGRlbGF5RG90UHJvZHVjdEc2JEYpL0krbW9kdWxlbmFtZUdGJUksVHlwZXNldHRpbmdHRig2JC1GMTYkRiQqJC1GMTYkKUYkSSMlVEdGJUYkRi1GPA==

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKnMtPzkq

e a componente de U ortogonal a este espa\303\247o \303\251 LCZJIlVHNiIiIiItSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YkSSxUeXBlc2V0dGluZ0c2JEYpSShfc3lzbGliR0YkNiRJIlBHRiRGIyEiIg==

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqNzw/OSo=

Em geral, este n\303\243o \303\251 o vetor zero, mesmo que os par\303\242metros livres 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, estavam todos a desaparecer. Outra forma de ver que U n\303\243o \303\251 no espa\303\247o coluna de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 tentar resolver a equa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ5RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9LUkjbW9HRiQ2LVEiPUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlYtRiw2J1EiVUYnRjhGOkY8Rj5GRA== para LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EieUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjcvRjZRJ25vcm1hbEYn. LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEsTGluZWFyU29sdmVGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJDRidGL0YyLUkjbW9HRiQ2LVEiLEYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYnUSJVRicvJSVib2xkR0YxL0YwRkUvRjNRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRmluRkE=

Error, (in LinearAlgebra:-LinearSolve) inconsistent system

O sistema \303\251 precisamente inconsistente porque U n\303\243o \303\251 no espa\303\247o coluna de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. Uma solu\303\247\303\243o alternativa da equa\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYnUSJ5RicvJSVib2xkR0YxL0YwUSZmYWxzZUYnL0YzUSVib2xkRicvJStmb250d2VpZ2h0R0Y9LUkjbW9HRiQ2LVEiPUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR0Y7LyUqc2VwYXJhdG9yR0Y7LyUpc3RyZXRjaHlHRjsvJSpzeW1tZXRyaWNHRjsvJShsYXJnZW9wR0Y7LyUubW92YWJsZWxpbWl0c0dGOy8lJ2FjY2VudEdGOy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlYtRiw2J1EiVUYnRjhGOkY8Rj5GRA== \303\251 obtida com LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21vR0YkNi1RIitGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkAvJSlzdHJldGNoeUdGQC8lKnN5bW1ldHJpY0dGQC8lKGxhcmdlb3BHRkAvJS5tb3ZhYmxlbGltaXRzR0ZALyUnYWNjZW50R0ZALyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGT0Y8LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJw==, a pseudo-inversa de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, obtida no Maple como QyQ+SSNDcEc2Ii1JLk1hdHJpeEludmVyc2VHRiU2JEkiQ0dGJS9JJ21ldGhvZEdGJUkncHNldWRvR0YlIiIi

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKilbYz0jKg==

Se LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== fosse invers\303\255vel, ter\303\255amos 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. Em vez disso, temos 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, a solu\303\247\303\243o de m\303\255nimos quadrados de comprimento m\303\255nimo. Em efeito, o vetor U \303\251 projetado sobre o espa\303\247o coluna de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, e a imagem inversa do comprimento m\303\255nimo \303\251 encontrado. Assim, o uso da pseudo-inversa nos permite ignorar componentes de U n\303\243o no espa\303\247o coluna de. A vers\303\243o do Maple de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2J1EiVUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1JI21vR0YkNi1RIitGJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZVL0Y2RjQvRjlRJ2l0YWxpY0YnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZD\303\251 PkkjVXBHNiItSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lR0YkSSxUeXBlc2V0dGluZ0c2JEYoSShfc3lzbGliR0YkNiRJI0NwR0YkSSJVR0Yk

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqKVtpPSMq

Que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2J1EiVUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1JI21vR0YkNi1RIitGJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZVL0Y2RjQvRjlRJ2l0YWxpY0YnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZD est\303\241 em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiM0YnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ \303\251 verificado pelo desaparecimento de 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, como vemos em LUkwZGVsYXlEb3RQcm9kdWN0RzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHNiRGJUkoX3N5c2xpYkdGKDYkKiRJIkNHRigiIiRJI1VwR0Yo

LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCIqW2EoPSMq

No entanto, LUklbXN1cEc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2J1EiVUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjctSSVtcm93R0YkNiQtSSNtb0dGJDYtUSIrRicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGU0ZBLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJw== n\303\243o \303\251 o fim de uma cadeia de comprimento 3, que come\303\247a com o vetor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2J1EiR0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjcvRjZRJ25vcm1hbEYn. A cadeia ainda precisa ser gerada de volta para baixo a partir de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2J1EiVUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjotRiM2JS1JI21vR0YkNi1RIitGJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdGNy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZVL0Y2RjQvRjlRJ2l0YWxpY0YnLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0ZD, como 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. A cadeia de comprimento 2 tamb\303\251m podem ser gerada com a pseudo-inversa, partindo de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EiR0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjQ=, calculando 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 como o fim da s\303\251rie em LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JJW1yb3dHRiQ2JC1JI21uR0YkNiRRIjJGJy9GM1Enbm9ybWFsRidGPC8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYn e recuando para o autovetor 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 em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+. Esses c\303\241lculos levam a uma matriz de transi\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= constru\303\255da pelos mesmos dispositivos usados anteriormente. QyQ/KEkia0c2IiIiIkYmSSJOR0YlSSV0cnVlRyUqcHJvdGVjdGVkR0MkPkkiVEdGJS1JJ01hdHJpeEc2JEYpSShfc3lzbGliR0YlNiM3KS1JMGRlbGF5RG90UHJvZHVjdEc2JEYpL0krbW9kdWxlbmFtZUdGJUksVHlwZXNldHRpbmdHRi82JC1GNDYkSSJDR0YlSSNDcEdGJUkiR0dGJS1GNDYkRj1GPi1GNDYkKiRGPCIiI0kjVXBHRiUtRjQ2JEY8RkVGRSZJJE5TMUdGJTYjJiZJJnBhaXJzR0YlNiNGJDYjRiYmRkk2IyZGTDYjRkRAJC8tSSVSYW5rR0YlNiNGLCIiKEMkLUkmcHJpbnRHRik2I0ZMWyEiIg==

NyQiIiMiIiQ=

Como n\303\263s tamb\303\251m mostramos anteriormente, verifica\303\247\303\243o que LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 uma matriz de transi\303\247\303\243o que coloca LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em sua forma de Jordan consiste em fazer com que a matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEjQVRGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSgmbWludXM7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkwtRiw2JVEjVEpGJ0YvRjJGOQ== seja nula. LCYtSTBkZWxheURvdFByb2R1Y3RHNiQlKnByb3RlY3RlZEcvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0c2JEYmSShfc3lzbGliR0YpNiRJIkFHRilJIlRHRikiIiItRiQ2JEYvSSJKR0YpISIi

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKj8oSDoqKQ==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH Finalmente, vamos abordar a quest\303\243o da gera\303\247\303\243o de uma matriz LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== com uma conhecida forma de Jordan LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. Isto \303\251 feito atrav\303\251s da defini\303\247\303\243o da matriz como 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, onde LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 a forma de Jordan dada, e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= \303\251 uma matriz de transi\303\247\303\243o cujas colunas ser\303\243o autovetores e autovetores generalizados. A matriz de Jordan LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 constru\303\255da no Maple com o comando JordanBlockMatrix cujo uso para gerar a matriz de Jordan na Tabela 1 est\303\241 ilustrado abaixo. JSFH LUkySm9yZGFuQmxvY2tNYXRyaXhHNiI2IzcmNyQiIiNGKDckRigiIiQ3JEYoIiIiRis=

LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciKkM/OSEqKQ==

O tamanho de um sub-bloco e seu autovalor associado \303\251 dado por uma lista e uma lista de tais listas que determina a matriz completa. A matriz de transi\303\247\303\243o LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== pode ser qualquer matriz conform\303\241vel n\303\243o singular . No entanto, se o determinante de LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== n\303\243o \303\251 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVElJnBtO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JFEiMUYnRi9GLw==, a matriz LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1cEdGJDYlLUkjbWlHRiQ2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvRjZRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlEtSSNtbkdGJDYkUSIxRidGPkYyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRj4= provavelmente ir\303\241 conter fra\303\247\303\265es, fazendo os c\303\241lculos mais tediosos. Por isso, selecionamos LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== aleatoriamente a partir de matrizes geradas com determinante LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVElJnBtO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjIyMjIyMjJlbUYnLyUncnNwYWNlR0ZDLUkjbW5HRiQ2JFEiMUYnRi9GLw== e entradas inteiras LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSNtbkdGJDYkUSIxRidGLy1GLDYtUSIsRidGL0YyL0Y2USV0cnVlRidGN0Y5RjtGPUY/L0ZCUSYwLjBlbUYnL0ZFUSwwLjMzMzMzMzNlbUYnLUZHNiRRIjBGJ0YvRkpGRkZKRi8=ou 2. Isto \303\251 feito com um c\303\263digo como o seguinte. JSFH QyY+SSJzRzYiIiIhISIiPyhJImtHRiUiIiJGKiIkKyZJJXRydWVHJSpwcm90ZWN0ZWRHQyQ+SSJNR0YlLUktUmFuZG9tTWF0cml4R0YlNiQiIigvSSpnZW5lcmF0b3JHRiU7RiciIiNAJC8tSSRhYnNHRi02Iy1JLERldGVybWluYW50R0YlNiNGMEYqQyU+RiQsJkYkRipGKkYqPihJInFHRiVGJEYwLUkmcHJpbnRHRi02JEYkRjBGJw==

NiQiIiItSSdNYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy9JJCVpZEdGKSIqO082LCo=

NiQiIiMtSSdNYXRyaXhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy9JJCVpZEdGKSIqc01pOCo=

A matriz adequada LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== \303\251 recuperada a partir do \303\255ndice impresso na frente da matriz. Por exemplo, se a \303\272ltima matriz \303\251 escolhida para LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==, pode ser extra\303\255da atrav\303\251s de PkkiUEc2IkkjcTNHRiQ=

SSNxM0c2Ig==

Tudo o que permanece \303\251 a constru\303\247\303\243o de 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. A base que coloca LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= em sua forma de Jordan n\303\243o \303\251 \303\272nica. Assim, a matriz de transi\303\247\303\243o LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== n\303\243o \303\251 \303\272nica. A Tabela 1 mostra a matriz LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== que foi usada para construir LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== para essa explora\303\247\303\243o. As matrizes de transi\303\247\303\243o LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= geramos com as diferentes bases que constru\303\255mos que n\303\243o foram necessariamente as mesmas que esta LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVEiUEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==. JSFH

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TTdSMApJNlJUQUJMRV9TQVZFLzExNDUyOTYxMlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI1IiKCIoIiIhRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiU= TTdSMApJNlJUQUJMRV9TQVZFLzEzNTIwODA5MlguJSlhbnl0aGluZ0c2IyYlJWJhbmRHNiQiIiEiIiI2IltnbCEiJCEhISMvIigiKCEiRikiIiNGKkYsRilGLEYqRixGKkYsRilGLEYpRixGKw== TTdSMApJNlJUQUJMRV9TQVZFLzEwMzQ5OTY4OFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI1IiKCIoISIiIiIhRidGJiIiIkYnRiciIiNGJkYnRidGKEYmRihGKEYpRiZGKUYoRidGKEYpRihGJkYoRihGKEYmRidGKEYpRihGJ0YpRidGKUYmRihGJ0YnRiZGJ0YoRidGKEYoRihGKEYpRiU= JSFH TTdSMApJNlJUQUJMRV9TQVZFLzQ0NTkxNzY3MlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI1IiKCIoIiIhIiIiIiIjRighIiJGKEYpRidGJ0YoRidGKEYmRidGKUYpRiZGKEYpRihGJ0YmRihGJ0YpRilGJkYmRilGKUYmRihGKEYmRidGJ0YnRidGJ0YnRihGJkYnRidGKEYnRiZGJ0YmRiU=TTdSMApJNlJUQUJMRV9TQVZFLzQ0NTkxNzkxMlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI1IiKCIoIiIhIiIjIiIlRighIiNGKEYpRiciIiQiIidGKEYqRiciIiJGKUYpRiZGKEYpRihGJyEiIkYqRidGJiEiJEYnRixGKUYmRixGKkYqRiZGJ0YnRidGJ0YnRidGKEYmRidGJ0YoRidGJkYnRiZGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzQ0NTg4NDkzNlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI1IiKCIoISM1IiIlISNdISMjKSIiIyEjYyIjWyEjOCIiJiEjZyEjKSoiIiIhI20iI2YiIzohIiciI3MiJD0iISIjIiMhKSEjcSEjOyIiKCEjeCEkRiJGKiEjJykiI3YiIidGOCIjSCIjWiEiIiIjSyEjRyIiKiEiJSIjViIjckZERiwhI1UhIiRGMUYtISNAIiIhISM5IiM4RiU=TTdSMApJNlJUQUJMRV9TQVZFLzg4NzUyMTY4MFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCMhIiIiIiNGJ0YnIiIhRilGKSIiIkYlTTdSMApJNlJUQUJMRV9TQVZFLzg4NzUyMTkyMFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCMhIiYiIiMhIiMhIiUiIiFGKyIiIkYrRiU=TTdSMApJNlJUQUJMRV9TQVZFLzg4NzUyMjE2MFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCMiIiYiIiNGKCIiJCIiISIiIkYqRipGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzg4NzUyMjQwMFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCMiIigiIiMiIiQiIiciIiIiIiFGLEYsRiU=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TTdSMApJNlJUQUJMRV9TQVZFLzg4OTQ5MjM0NFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiIUYmRiZGJkYmIiIiRiZGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzg4OTQ5MjU4NFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiIUYmRiZGJiIiIkYmRiZGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzg4OTQ5MjgyNFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiIUYmRiYiIiJGJkYmRiZGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzg4OTQ5MzA2NFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiIUYmIiIiRiZGJkYmRiZGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzg4OTQ5MzMwNFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiISIiIkYmRiZGJkYmRiZGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzg4OTQ5MzU0NFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiIiIiIUYnRidGJ0YnRidGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzg4OTQ5MzY2NFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCYlInhHNiMiIiImRic2IyIiIyZGJzYjIiIkJkYnNiMiIiUmRic2IyIiJiZGJzYjIiInJkYnNiMiIihGJQ==TTdSMApJNlJUQUJMRV9TQVZFLzg5MDUxMDQ0OFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiIUYmRiZGJkYmRiZGJkYlTTdSMApJNlJUQUJMRV9TQVZFLzg5MDUxNzc2OFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCwwJiUieEc2IyIiIiEjRSZGKDYjIiIjISNLJkYoNiMiIiQiI1EmRig2IyIiJSEjVCZGKDYjIiImIiM6JkYoNiMiIiciI0ImRig2IyIiKCEiKEYmIiIhLDBGJyIjX0YsIiNrRjAhI3dGNCIjIylGOCEjSUY8ISNZRkAiIzlGJkZFLDBGJyIjRUYsIiNLRjAhI1FGNCIjVEY4ISM6RjwhI0JGQEZCRiU=TTdSMApJNlJUQUJMRV9TQVZFLzg5MDUxODcyOFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCwwJiUieEc2IyIiIiEjNSZGKDYjIiIjISM4JkYoNiMiIiQiIzomRig2IyIiJSEjOyZGKDYjIiImIiInJkYoNiNGOyIiKiZGKDYjIiIoISIkLDBGJ0Y2RixGOkYwISInRjRGQUY4ISIjRjwhIiVGP0YqLDBGJyEjXUYsISNnRjAiI3NGNCEjeEY4IiNIRjwiI1ZGP0YvLDBGJyEjIylGLCEjKSpGMCIkPSJGNCEkRiJGOCIjWkY8IiNyRj8hI0AsLkYnRi5GLEYqRjBGRUY0Ri5GOCEiIkY8RlcsMEYnISNjRiwhI21GMCIjISlGNCEjJylGOCIjS0Y8IiNbRj8hIzksMEYnRmhuRiwiI2ZGMCEjcUY0IiN2RjghI0dGPCEjVUY/IiM4RiU=TTdSMApJNlJUQUJMRV9TQVZFLzg5MDUwMjYyNFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI1IiKCIoIyIlUTciJTI5IyEkMyNGKCMiJFojRigjISRMJiIlOUcjIiNsIiRRKiMiJCpIRi8jISM4IiQtJUYpIyIlXjZGKCMiJC8kRigjISRHJEYoIyIjUyIkcCUjIiQlPUYoIyEiKSIkLCNGK0Y6IyIlWTVGKCMiJHooRi8jISMmKkYyIyEkUCVGLyMiIz5GN0YtRjxGSCMiJVpSIiVHYyMiJDAjIiV3PSMiJFYqRlIjISNUIiQvKUYwRj5GSkZTIyIlLD1GVSMhJDoiRlUjIiImIiRvI0YzRkFGTEZWRmduIyIlKjQmRlIjIiNCRlpGNUZDRk5GWEZpbkZebyMiJCh6RlpGJQ==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TTdSMApJNlJUQUJMRV9TQVZFLzg5MzgyNTIzMlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCMhIiUiIzgjISIiRigjIiInRigjIiM5RigjISIoRihGLSMiIiJGKEYlTTdSMApJNlJUQUJMRV9TQVZFLzg4OTQ3Mzg2NFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCMhIigiI0UiIiFGKUYpRilGKSIiIkYlTTdSMApJNlJUQUJMRV9TQVZFLzkxMjE0ODgzMlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI1IiKCIoIiIhRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiU=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TTdSMApJNlJUQUJMRV9TQVZFLzkxNDE4NjM1MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiIiIiIUYnIyEiIyIiJCMiIiVGKiMhIiVGKkYtRiU=TTdSMApJNlJUQUJMRV9TQVZFLzkxNDE4NjQ3MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiISIiIkYmIyEiJSIiJCMhIiJGKiMhIiNGKiNGJ0YqRiU=TTdSMApJNlJUQUJMRV9TQVZFLzkxNDE4NjU5MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiIUYmIiIiIyIiJiIiJCMhIiJGKiMiIiVGKiMhIiNGKkYlTTdSMApJNlJUQUJMRV9TQVZFLzkxNDE5MzU1MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCMhIiIiIiMiIiEiIiJGKEYnRihGKUYlTTdSMApJNlJUQUJMRV9TQVZFLzkxNDE5MzY3MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiIkYmIiIhISIjRiZGKCEiIkYlTTdSMApJNlJUQUJMRV9TQVZFLzkxNDE5NDE1MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCwmJSJ1RyMhIiIiIiMlInZHIiIiRitGJywmRidGKkYrISIjLCZGJ0YpRitGLEYtLCRGK0YpRiU=TTdSMApJNlJUQUJMRV9TQVZFLzkxNDE5NTM1MlgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCYlInRHNiMiIiIsLkYmISIlJkYnNiMiIiRGLiZGJzYjIiIlISIiJkYnNiMiIiZGLiUidUcjISImIiIjJSJ2R0YyRixGL0YzLC5GJiEiI0YsRilGL0YpRjNGOUY2IyEiJEY5RjpGPCwuRiYiIilGLEY4Ri9GOUYzRjhGNiMiIzhGOUY6RjxGJQ==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TTdSMApJNlJUQUJMRV9TQVZFLzkyMTg3NTQ0OFgqJSlhbnl0aGluZ0c2IkYlW2dsISMlISEhIigiKCIiIUYmRiZGJkYmRiZGJkYlTTdSMApJNlJUQUJMRV9TQVZFLzg5MTUyOTcyMFgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI1IiKCIoIiIhRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiZGJkYmRiU=TTdSMApJNlJUQUJMRV9TQVZFLzg5MDE0MjAyNFguJSlhbnl0aGluZ0c2IyYlJWJhbmRHNiQiIiEiIiI2IltnbCEiJCEhISMvIigiKCEiRikiIiNGKkYsRilGLEYqRixGKkYsRilGLEYpRixGKw==TTdSMApJNlJUQUJMRV9TQVZFLzkwMTExMzYxNlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI1IiKCIoIiIhIiIiRidGJkYnRiciIiNGKCEiIkYnRiZGKEYoRiZGJkYmRidGKEYpRilGJkYnRilGKUYpRihGJ0YmRiZGKEYmRidGJ0YmRiZGKEYmRidGJ0YnRiZGKUYmRiZGJ0YmRilGJkYmRiU=TTdSMApJNlJUQUJMRV9TQVZFLzkxMzYyMzQ3MlgsJSlhbnl0aGluZ0c2IkYlW2dsISIlISEhI1IiKCIoIiIiIiIjRiYiIiFGKEYnRiZGJyEiIkYnRilGJkYpRiZGJkYmRihGJkYmRilGKEYmRidGJ0YpRiZGJ0YpRidGKEYoRiZGJkYnRiZGJkYoRilGJ0YoRiZGJkYoRihGJkYpRihGKUYoRiU=