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Homework Help: Proving that the eigenvalues of a Hermitian matrix is real

  1. Dec 7, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove that the eigenvalues of a Hermitian matrix is real.

    The website says that "By Product with Conjugate Transpose Matrix is Hermitian, v*v is Hermitian. " where v* is the conjugate transpose of v.

    2. Relevant equations

    3. The attempt at a solution

    I'm not sure why that is true. v*Av is equal to v*v, and v*Av is a Hermitian matrix. Intuitively, v*v seems like a Hermitian matrix, but I need a real theorem that would show that.
  2. jcsd
  3. Dec 7, 2012 #2

    D H

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    Staff Emeritus
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    Do you really need a proof that v*v is Hermitian? Some things are just obvious. This is one of those things.
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