Jordan Decomposition to Schur Decomposition

  • Thread starter azdang
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Homework Statement


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.


Homework Equations


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


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.
 

Answers and Replies

  • #2
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No ideas? Sorry to be impatient. I just really am not getting anywhere.
 

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