Let N be an k*k nilpotent matrix with nilpotency index k i.e. but . I want to show that (transpose of N) is similar to N.

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- Aug 6th 2013, 12:39 PMHumansimilar to its transpose
Let N be an k*k nilpotent matrix with nilpotency index k i.e. but . I want to show that (transpose of N) is similar to N.

- Aug 6th 2013, 02:24 PMDrexel28Re: similar to its transpose
I mean, since or contain all the eigenvalues of you can conjugate to put it in Jordan canonical form and then you only have to note that the Jordan matrix is similar to its transpose.