SAS^(1) is Block Upper Triangular (Blocks of size <= 2) [Possible Schur Decomp]by brru25 Tags: block, diagonal, induction, schur, upper triangular 

#1
Nov1709, 01:26 PM

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 



#2
Nov1809, 02:08 AM

HW Helper
P: 3,309

so if S is unitary then
[tex] S^{1} = (S^{T})^* [/tex] 


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