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

  1. 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. jcsd
  3. lanedance

    lanedance 3,307
    Homework Helper

    so if S is unitary then

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