Matrix with trace zero

Asked Jul 07 '14 at 16:18

Active Jul 07 '14 at 16:18

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Question is that :

Suppose a matrix $A\in M_n(\mathbb{C})$ is a commutator by which i mean $A=BC-CB$ for some $B,C\in M_n(\mathbb{C})$ then we see that Trace of $A$ is $0$

But Suppose a matrix is of trace zero can we say that it is commutator?

I have tried seeing this for $2\times 2$ matrices and end up with nothing reasonable..

I would be thankful if some one can suggest me a way to proceed in this case.

asked Jul 07 '14 at 16:18

1

Perhaps this paper would be of interest. The question that you are interested in appears to be the subject of Theorem 3. – Peter Woolfitt Jul 07 '14 at 16:27
@PeterWoolfitt : how did you get that? Thank you anyways :) :) – Jul 07 '14 at 16:29
@copper.hat : Thank you :) – Jul 07 '14 at 16:34
You are very welcome! – copper.hat Jul 07 '14 at 16:36

Matrix with trace zero

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