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Inner product of complex numbrs

  1. Oct 27, 2012 #1
    I would like if someone could either verify or clarify my thinking about inner products.

    There is a matrix, V that is m x n, that is made up of complex numbers. When matrix V is multiplied by its hermitian then the product is a matrix with the same integer down the main diagonal (i.e. Eigenvalues are all the same).
  2. jcsd
  3. Oct 28, 2012 #2
    If you mean by its Hermitian the conjugate transpose. There are matrices that are self adjoined, and don't change under that operation. When you multiply such a matrix by its conjugate transpose the eigenvalues are squared.
  4. Oct 28, 2012 #3
    What do you mean by self adjoining?
  5. Oct 30, 2012 #4
    The definition of a self adjoint or Hermitian matrix is, that the matrix is the same after mirroring on the main diagonal and complex conjugation. What you mean by Hermitian of a matrix I don't know.
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