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SAS^(-1) is Block Upper Triangular (Blocks of size <= 2) [Possible Schur Decomp]

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Nov17-09, 01:26 PM
P: 29
1. The problem statement, all variables and given/known data

Let A be an nn real matrix. Show that there exists S such that SAS-1 is block upper triangular with diagonal blocks of size at most 2.

2. Relevant equations

BUP = block upper triangular

3. The attempt at a solution

It sounds a lot like the Schur decomposition (which is proven by induction), but the only difference is that here the question is asking for an S such that SAS-1 is BUP, but the Schur decomposition says that SAS* is BUP
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Nov18-09, 02:08 AM
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P: 3,307
so if S is unitary then

[tex] S^{-1} = (S^{T})^* [/tex]

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