Unformatted text preview: A on Q 5 . We found that Q 5 is the direct sum of two T –invariant subspaces V 1 and V 2 . The subspaces V 1 is one dimensional, spanned by v 1 D 2 6 6 6 6 4 4 1 8=3 3 7 7 7 7 5 , and Av 1 D v 1 . The subspace V 2 is four dimensional, and generated as a KŒxŁ –module by v 2 D 2 6 6 6 6 4 3 3 1 3 7 7 7 7 5 . The period of V 2 is .x ± 1/.x ± 2/ 3 . We get the Jordan canonical form by computing the primary decomposition of V 2 , V 2 D V 2 Œx ± 1Ł ˚ V 2 Œx ± 2Ł . The subspace V 2 Œx ± 1Ł is one dimensional, and spanned by w 1 D .A ± 2E/ 3 v 2 D 2 6 6 6 6 4 3 ± 3 2 3 7 7 7 7 5 : The subspace V 2 Œx ± 2Ł...
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 Fall '08
 EVERAGE
 Linear Algebra, Algebra, Jordan Canonical Form, W Œx, V2 D V2, .A 2E/3 v2

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