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Unformatted text preview: A is diagonal. (c) The minimal polynomial of A has no multiple roots; that is, the minimal polynomial is a product of distinct linear factors. (d) The elementary divisors of A are linear. 8.7.5. Recall that a matrix N is nilpotent if N k D for some k , Let A 2 Mat n .K/ , and suppose that the characteristic polynomial of A factors into linear factors in Kx . Show that A is the sum of two matrices A D A C N , where A is diagonalizable, N is nilpotent, and A N D NA . 8.7.6. Let N 2 Mat n .K/ be a nilpotent matrix. (a) Show that N has characteristic polynomial N .x/ D x n . (b) Show that the Jordan canonical form of N is a direct sum of Jordan blocks J m .0/ ....
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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