Hi

I have a square matrix A whose entries are non negative. I have another matrix B obtained from A by replacing one (or more) column(s) of A by its negative. Is there a special case where corresponding matrix powers , A^k and B^k where k>1, could span the same vector space?

eg.

A=[1, 2; 3, 4]

B=[1, -2; 3, -4]

Thanks