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Orthogonal Matrices

  1. Apr 23, 2006 #1
    I've got a question regarding orthogonal matrices. I am given an orthogonal matrix M, and a symmetric matrix A. I need to prove that (M^-1)*A*M is also symmetric (all of the matrices are n x n). I know that for an orthogonal matrix, its inverse is equal to its transpose. Can anyone give me some hints on how to begin this proof?
  2. jcsd
  3. Apr 23, 2006 #2


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    It seems to me that the obvious first thing to do would be to look at the transpose of (M^-1)*A*M.
  4. Apr 23, 2006 #3
    Thanks for the tip. I believe the transpose of that matrix would also be (M^-1)*A*M, since (AB)^T = B^T * A^T. And if a matrix equals its own transpose, doesn't that make it symmetric?

    Well, I guess that in my commentary, I've accidentally solved the problem. Thanks.
  5. Apr 24, 2006 #4


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    Don'cha hate when that happens!
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