Hi,
I think you are confused and mixing things up. First :
There is no justification to be presented. ##T## is diagonalisable, saying ##T' = D## is just a matter of identification in my previous message.
Then I think you are trying to proove the spectral theorem with T. If you want to see how...
Hello,
before answering your question I would like to draw your attention on a sloppy statement of the PDF file you put in attachement. Right before eq. (40) it says that all square matrices are diagonalisable, which is obviously not true. Take ##\begin{pmatrix} 5 & 1 \\ 0 & 5 \end{pmatrix} ##...