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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 rst 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 Kx module with period a power of .x / . 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 /x 1 D x , .T /x 2 D x 1 , etc. We nally come to a vector x r such...
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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