1. The problem statement, all variables and given/known data in light of the gram-schmidt orthogonalization process, if A: Rn -> Rn and we have a basis of Rn of eigenvectors of A, can't we just orthonormalize them and get a matrix P such that P-1=PT and thus PTAP is diagonal? 2. Relevant equations 3. The attempt at a solution I believe the answer to this is yes, but I'm not sure how to prove this. Any ideas would be appreciated, thanks!