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

by brru25
Tags: block, diagonal, induction, schur, upper triangular
 P: 29 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
 HW Helper P: 3,309 so if S is unitary then $$S^{-1} = (S^{T})^*$$

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