1. The problem statement, all variables and given/known data Suppose H is an n by n real symmetric matrix. v is a real column n-vector and H^(k+1)v = 0. Prove that Hv = 0 3. The attempt at a solution Since H is a real symmetric matrice we can find an orthogonal matrix Q to diagnolize it: M = Q transpose. MA^(k+1)Qv = 0 Implying A^(k+1)Qv = 0 This is where I'm stuck i'm not sure how to proceed. I'm pretty sure its not possible to somehow get Q remove from the equation because that implies v or A would have to be 0 but this does not follow since I can easily cook up an example were there is a symmetric matrix to a power were H^(K+1)v=0 and v != 0. Thus any hints would be appreciated.