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Help simplify the matrix equation

  1. Dec 6, 2009 #1
    I encounter a problem when simplifying the following equation, can anyone give a hint:)

    Let A denote an orthonormal matrix, X be a symmetric matrix.

    diag(A) is an operator that creates a diagonal matrix of A.

    Then, my problem is how to simplify the equation:

    [tex]A^{-1} \cdot diag(A \cdot X \cdot A^{-1}) \cdot A[/tex]
     
    Last edited: Dec 6, 2009
  2. jcsd
  3. Dec 6, 2009 #2

    HallsofIvy

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    "diag(A) is an operator that creates a diagonal matrix of A."

    That doesn't tell us enough. There are many ways to make a diagonal matrix out of A, for example, just setting all non-diagonal values equal to 0. Do you mean "diag(A) is a diagonal matrix similar to A"? In that case, are we to assume that A is diagonalizable?
     
  4. Dec 6, 2009 #3
    Sorry, I'll clarify the defitioon of diag (A).

    diag(A) is a square matrix in which the entries outside the diagonal are all zero, and its diagonal entries are the diagonal of A.
     
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