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Jordan Decomposition to Schur Decomposition

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Let A be a complex or real square matrix. Suppose we have a Jordan decomposition A = XJX-1, where X is non-singular and J is upper bidiagonal. Show how you can obtain a Schur Decomposition from a Jordan Decomposition.

    2. Relevant equations
    Schur Decomposition: A = QTQ*, where Q is unitary/orthogonal and T is upper triangular with the eigenvalues of A on the diagonal.

    3. The attempt at a solution
    I'm really not sure at all what to do. Because Q is orthogonal, Q*=Q-1. I'm not sure if that plays in somehow.

    I've been trying to use SVDs or QR decompositions of X or J to get there, but I've had no luck. Does anyone have any suggestions? Thank you so much.
  2. jcsd
  3. Mar 30, 2009 #2
    No ideas? Sorry to be impatient. I just really am not getting anywhere.
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