1. The problem statement, all variables and given/known data let p(x) = summation(from i=0 to k) aix^i matrix polynomial for A is defined as p(A) = summation(i=0 up to k) aiA^i Show that if (lambda, x) is an eigenpair of A then (p(lambda), x) is an eigenpair of p(A) 2. Relevant equations 3. The attempt at a solution I pretty much have no idea where to start. I thought I could use Ax = lambda x like you would if you were proving that lambda^2 is an eigenvalue of A^2, etc, but I'm not sure how to get the p(A) bit?