
matrix powers
Hi,
If I am given an nxn matrix A and the characteristic polynomial of A is (X6)^n for A. Is there anyway to work out which of the factors is the minimum polynomial for A by DIRECTLY raising the matrix (AXIn) to the various powers of the factors (rather than calculating the powers the long way!).
Thanks.

Let's see if i understand. You wish to find the minimum polynomial without effort?
I don't think there is a royal path here. You have to find (A6I)^2, (A6I)^3,... until you get a zero.