# similar to its transpose

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• August 6th 2013, 11:39 AM
Human
similar to its transpose
Let N be an k*k nilpotent matrix with nilpotency index k i.e. $N^k=0$ but $N^{k-1} \neq 0$ . I want to show that $N^t$ (transpose of N) is similar to N.
• August 6th 2013, 01:24 PM
Drexel28
Re: similar to its transpose
I mean, since $\mathbb{R}$ or $\mathbb{C}$ contain all the eigenvalues of $N$ 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.