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Orthogonal and symmetric matrices

  1. Jun 8, 2010 #1
    I guess this is a basic question.
    Let´s say that If I am given a matrix X it is possible to form a symmetric matrix by computing [itex]X+X^{T} [/itex].

    But how can I form a matrix which is both symmetric and orthogonal? That is:
  2. jcsd
  3. Jun 9, 2010 #2


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    You have implicitly stated that M is real. In this case I think only the identity matrix matches your requirements.
  4. Jun 9, 2010 #3
    And also diagonal matrix with 1 or -1 at diagonal. Any more?
  5. Jun 10, 2010 #4
    Thanks for the answers.
    I just noticed that unfortunately I stated my problem incorrectly.

    Starting from a matrix, I wanted to find another matrix which is symmetric (not Hermitian!) and unitary. That is:


    Here [tex]M^{T}[/tex] means "transpose", while [tex]M^\dagger[/tex] means "conjugate transpose".
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