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Orthogonal transformation of matrix

  1. Apr 6, 2006 #1
    I have a question on matrix norms and orthogonal transformations. The 2-norm in invariant under orthogonal transformation, for if Q^T*Q=I. But i have trouble showing that for orthogonal Q and Q^H with appropriate dimensions

    || Q^H*A*Q ||2 =|| A ||2
  2. jcsd
  3. May 23, 2006 #2
    The 2-norm of A returns the square-root of the maximum absolute eigenvalues of A^HA. So check, does (Q^HA*Q)^HQ^HA*Q preserve the absolute eigenvalues of A^HA?
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