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Math Help - hermitian matrix over C

  1. #1
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    hermitian 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.
    Last edited by guin; March 1st 2011 at 01:23 AM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by guin View Post
    Do anyone has an example of nxn hermitian matrix over complex which has n distinct eigenvalues?
    If can make the n as small as possible. Thank you
    If you want a simple one:
    \displaystyle \left [ \begin{array}{ccc} 1 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & 5 \end{array} \right ]

    You can add window dressing to it, but it fits what you asked for. Did you want one less "trivial" to work on yourself?

    -Dan
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Although the question has been already solved by topsquark , I'd like to add that D=\textrm{diag}(\lambda_1,\ldots,\lambda_n)\in\mat  hbb{C}^{n\times n} is hermitian iff \lambda_i\in\mathbb{R} for all i=1,\ldots,n. So, all diagonal real matrices with \lambda_i\neq \lambda_j for all i\neq j are hermitian and have n distinct eigenvalues.
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