Orthogonal and symmetric matrices

  • Thread starter mnb96
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  • #1
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Hello,
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:
[tex]M=M^{T}=M^{-1}[/tex].
 

Answers and Replies

  • #2
marcusl
Science Advisor
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You have implicitly stated that M is real. In this case I think only the identity matrix matches your requirements.
 
  • #3
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And also diagonal matrix with 1 or -1 at diagonal. Any more?
 
  • #4
713
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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:

[tex]M=M^{T}[/tex]
[tex]MM^\dagger=I[/tex]

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

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