solving a system of non-linear equations

[Mathes]

Hey,

I have a little mathematical question here.
Suppose we have two matrices A and B (both of the dimension N x N). Now we want to check whether or not another matrix P (permutation matrix) exists, so that
P*A*(P^T) = B

Does anyone have a good algorithm (with detailed explanation)?
I checked wikipedia, but I don't quite understand which algorithm is
appropriate here... First time I'm dealing with such a problem.

And I cant use any lib (like GSL), because I'd like to use the algorithm
with parallel processing (A and B might get large 10000 x 10000 and more).

Any advice for a good algorithm would be great.

Thanks in advance
Mathes

[hamsterman]

http://en.wikipedia.org/wiki/Permutation_matrix#Solving_for_P
Though you should start with checking traces of A and B (they should be equal). Note, P^T = P^-1 for a permutation matrix.

Also, I suggest that in the future you use http://math.stackexchange.com/ for that sort of questions.

[Mathes]

Thanks hamsterman.

Maybe I should check the English version of Wikipedia more often. Much more informative
than the German one...

And thanks for the site. Next math question will go there ;-)