(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Homework Help: Eigenvalue/Eigenvector proof

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