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Unformatted text preview: rational canonical form of A is ± C a 1 .x/ C a 2 .x/ ² D 2 6 6 6 6 4 1 0 0 0 0 0 0 ± 8 1 0 0 20 0 1 0 ± 18 0 0 1 7 3 7 7 7 7 5 : Now we consider how to ﬁnd a basis with respect to which the transformation T determined by multiplication by A is in rational canonical form. Q 5 D V 1 ˚ V 2 , where each of V 1 and V 2 is invariant under T and cyclic for T . The subspace V 1 is one–dimensional and the subspace V 2 is four– dimensional. We obtain cyclic vectors for these two subspaces using the 2 Examples of computations of rational canonical form can be found in the notebook CanonicalFormExamples.nb , also available on my webpage....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra

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