archiver 8

Tuesday, February 14, 2006

square matrix and it's transpose are similar

"Are a matrix and it's transpose similar?"
three proofs in the sci.math (google groups) thread.

proof 1 : Divide and Conquer Method: rational canonical form and with that minimal polynomial determines companion matrix.

proof 2 : Divide and Conquer Method: Jordan normal form decomposition J = D + N and showing that N is similar to transpose of N by permutation.

Above two are examples of Divide And Conquere that is not Divide Into Cases. (ways: direct sum decomposition. linear sum)

proof 3 : symmetry in computing g_1,...

tag: math. linear. algebra. proof. divide

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