Do anyone has an example of nxn hermitian matrix with complex entries which has repeated eigenvalues?

If can make the n as small as possible. Thank you

Sorry for the mistake I made before in my question.

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- Feb 28th 2011, 07:59 PMguinhermitian matrix over C
Do anyone has an example of nxn hermitian matrix with complex entries which has repeated eigenvalues?

If can make the n as small as possible. Thank you

Sorry for the mistake I made before in my question. - Feb 28th 2011, 08:33 PMtopsquark
- Feb 28th 2011, 11:25 PMFernandoRevilla
Although the question has been already solved by

**topsquark**, I'd like to add that $\displaystyle D=\textrm{diag}(\lambda_1,\ldots,\lambda_n)\in\mat hbb{C}^{n\times n}$ is hermitian iff $\displaystyle \lambda_i\in\mathbb{R}$ for all $\displaystyle i=1,\ldots,n$. So, all diagonal real matrices with $\displaystyle \lambda_i\neq \lambda_j$ for all $\displaystyle i\neq j$ are hermitian and have $\displaystyle n$ distinct eigenvalues.