Number of matrices n x n with n^2 different elements which have that same characteristic polynomial

[Max A.]

On 1/9/07, Artur <grafix at csl.pl> wrote:
> Problem is for 4 x 4 because loops have 4! 12!=344881152000 steps and is
> out of possibility of my computer

Actually, you can fix elements on the main diagonal (as simultaneous
permutations of columns and rows do not change the characteristic
polynomial) and get out of factor 4!. But that still leave 12!
variants to go.

Max