Applying similarity transform to a matrix $A$ gives: $$M=P^{-1}AP$$ $M$ and $A$ have same eigenvalues. What is the way to to find $P$ such that $M$ is diagonally dominant case of $A$? $M$ is diagonally dominant if
$$|{m_{ii}}| \ge \sum\limits_{j \ne i} | {m_{ij}}|\quad {\rm{for \quad all}}\quad i,{\mkern 1mu} $$ Note: I want $P$ to be something other than eigenvectors of $A$
EDIT:
Some eigenvalues of $A$ might be zero.