If I have a hermitian matrix whose eigen values are non negative, and the trace=0, must the matrix=0?
I gather that the eigen values must all be 0, but I could not find an example of a hermitian matrix with all 0 eigenvalues.
Thanks for your help.
2026-04-01 11:13:17.1775041997
Hermitian matrices, non-zero
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A Hermitian matrix is diagonalizeable. If all its eigenvalues are $0$, then it is similar to a diagonal matrix with zeros on the diagonal (i.e. the zero matrix), thus it is the zero matrix.