Let A be a complex or real square matrix. Suppose we have a Jordan decomposition A = $\displaystyle XJX^{-1}$, where X is non-singular and J is upper bidiagonal. Show how you can obtain a Schur Decomposition from a Jordan Decomposition.

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

I'm really not sure at all what to do. Because Q is orthogonal, Q*=$\displaystyle Q^{-1}$. 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.