1. The problem statement, all variables and given/known data Prove that if A is an nxn positive definite symmetric matrix, then an orthogonal diagonalization A = PDP' is a singular value decomposition. (where P' = transpose(P)) 2. The attempt at a solution. I really don't know how to start this problem off. I know that the singular value decomposition is of the form A = UEV' where E will be an nxn matrix containing the singular values of A, and in this case the eigenvalues of A as well. But that's about it. Any help would be greatly appreciated!