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

1. Nov 17, 2009

### 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

2. Nov 18, 2009

### lanedance

so if S is unitary then

$$S^{-1} = (S^{T})^*$$