Block Diagonal Matrix and Similarity Transformation

[nigelscott]

I am looking at page 2 of this document.https://ocw.mit.edu/courses/chemist...stry-ii-fall-2008/lecture-notes/Lecture_3.pdf

How is the transformation matrix, ν, obtained? I am familiar with diagonalization of a matrix, M, where D = S^-1MS and the columns of S are the eigenvectors of M but this doesn't appear to be the case here.

Any help would be appreciated.

 

[jasonRF]

Some matrices cannot be diagonalized. In such cases the "best" you can do is to make them block-diagonal; in linear algebra this is called the Jordan Form. To me it looks like this is what the notes are talking about.

EDIT: right after posting, I remembered that the Jordan form has upper-triangular blocks, so the notes are not doing that...

Jason