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

brru25

1. The problem statement, all variables and given/known data

Let A be an n×n 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

lanedance

so if S is unitary then

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