given the similarity relation between $A$ and $B$ matrices;
$ A = L^{-1} B L $
if $A$ and $B$ are given, what is the best way to compute the similarity transformation matrix $L$?
given the similarity relation between $A$ and $B$ matrices;
$ A = L^{-1} B L $
if $A$ and $B$ are given, what is the best way to compute the similarity transformation matrix $L$?
Answering the unanswered before it gets too old to be pushed to the front page. One possible answer is already given by Arturo Magidin in the comment.
If $A$ and $B$ are similar then they are also similar to a canonical form (typically the Jordan form). Thus, one way to find the similarity matrix is to reach to the canonical form, say $J$, from both matrices via $Q^{-1}AQ = J = P^{-1}BP$
Then, one can use either $A = (QP^{-1})B(QP^{-1})^{-1}$ or $B = (PQ^{-1})A(PQ^{-1})^{-1}$