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Math Help - "unitary diagonalization"(?)

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    "unitary diagonalization"(?)

    Is every matrix diagnosable, was unitary unitary diagonalization?

    I think it's not true... especially over field C, but I can't point on that matrix.

    Thank you(again!)
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  2. #2
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    Quote Originally Posted by Also sprach Zarathustra View Post
    Is every matrix diagnosable, was unitary unitary diagonalization?

    I think it's not true... especially over field C, but I can't point on that matrix.

    Thank you(again!)

    If you meant to ask whether any diagonalizable matrix is unitarily diagonalizable then the answer is no:

    Theorem: A square complex matrix is unitarily diagonalizable iff it is normal.

    Tonio
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