Register to reply

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

Share this thread:
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
Phys.Org News Partner Science news on
Suddenly, the sun is eerily quiet: Where did the sunspots go?
'Moral victories' might spare you from losing again
Mammoth and mastodon behavior was less roam, more stay at home
Nov18-09, 02:08 AM
HW Helper
P: 3,307
so if S is unitary then

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

Register to reply

Related Discussions
Complex and upper triangular matrices Calculus & Beyond Homework 5
Inverse of Upper Triangular Matrix Linear & Abstract Algebra 5
Force needed to keep block from moving on frictionless triangular block Introductory Physics Homework 1
Upper Triangular Matrix Calculus & Beyond Homework 4
Some clarification on upper triangular matrices please. Linear & Abstract Algebra 2