I am having trouble finding the schur factorization of the following matrix:
$A=\begin{pmatrix}3&8 \\ -2&3 \end{pmatrix}$
I followed an algorithm in the book, as well as computing an answer via Octave/Matlab. I did the following:
[U,T] = schur(A) where $U$ will be a unitary matrix and $T$ will be an upper triangular matrix.
Which gave me:
$U=\begin{pmatrix}1&0 \\ 0&1 \end{pmatrix}$ and $T=A$
$T=A$ is not upper triangular -- schur's factorization is supposed to give us an upper triangular matrix...
- What went wrong? Is a schur factorization possible for every square matrix (it should be according to wikipedia on schur decomposition
Thanks for all the help!