Unformatted text preview: , J is similar to J t . So, by transitivity of similarity, A is similar to A t . Computing the Jordan canonical form We will present two methods for computing the Jordan canonical form of a matrix. First method. The ﬁrst method is the easier one for small matrices, for which computations can be done by hand. The method is based on the following observation. Suppose that T is linear operator on a vector space V and that V is a cyclic KŒxŁ –module with period a power of .x ² ±/ . Then V has (up to scalar multiples) a unique eigenvector x with eigenvalue ± . We can successively solve for vectors x ± 1 ;x ± 2 ;::: satisfying .T ² ±/x ± 1 D x , .T ² ±/x ± 2 D x ± 1 , etc. We ﬁnally come to a vector x ± r such...
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 Fall '08
 EVERAGE
 Linear Algebra, Algebra, Jordan Canonical Form, Jm .0/

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