Let $A$ be an $n$ x $n$ matrix with complex entries such that Trace$(A)$ = $0$. Then $A$ is similar to a matrix with $0$ in the diagonal entries

Asked Apr 20 '14 at 16:58

Active Apr 20 '14 at 16:58

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Let $A$ be an $n$ x $n$ matrix with complex entries such that Trace$(A)$ = $0$. Then how to show that $A$ is similar to a matrix with $0$ in the diagonal entries?

asked Apr 20 '14 at 16:58

liesel

Hint: Similar matrices represent the same linear operator under two different bases. The trace, and in particular the characteristic polynomial, are properties of the operator. – Joseph Zambrano Apr 20 '14 at 17:26
2

I have proved this in another thread. See the second paragraph. – user1551 Apr 20 '14 at 17:28
Does this answer your question? Complex matrices with trace=0 – Majid May 15 '20 at 00:02

Let $A$ be an $n$ x $n$ matrix with complex entries such that Trace$(A)$ = $0$. Then $A$ is similar to a matrix with $0$ in the diagonal entries

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