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Let $A$ be a $n\times n$ matrix with complex entries such that $\operatorname{Trace}(A) = 0$. Show that $A$ is similar to a matrix with $0$'s in the diagonal entries. I think I have to use Schur's Lemma , but this is not helping me much .

Thanks for any help .

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I could write the answer but I think it's better for you to check directly here http://www.cs.berkeley.edu/~wkahan/MathH110/trace0.pdf . There are there some references to nice generalizations.

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Thanks for the referrence . –  Ester May 21 '12 at 18:10

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