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Prove eigenvalues are real

  1. Jul 14, 2009 #1
    Given a 4x4 non-Hermitian matrix, is there any method I can use to prove the eigenvalues are real, aside from actually computing them?

    I'm looking for something like the converse of the statement "M is Hermitian implies M has real eigenvalues".

    When can one say that the eigenvalues of a given matrix are real?
  2. jcsd
  3. Jul 14, 2009 #2


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    Gold Member

    In general, the eigenvalues of a non-Hermitian matrix can be complex. You would need to compute them.
  4. Jul 15, 2009 #3
    OK, I'm not surprised. Thanks anyways.
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