If N is any k*k nilpotent matrix i.e;N^k=0 but N^k-1 not equal to 0 ,then show that transpose of N is similar to N.Hence deduce that every complex n*n matrix is similar to its transpose.

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- December 12th 2009, 01:48 AMmath.djSimilar matrices
If N is any k*k nilpotent matrix i.e;N^k=0 but N^k-1 not equal to 0 ,then show that transpose of N is similar to N.Hence deduce that every complex n*n matrix is similar to its transpose.