Suppose that A e Mnxn(R) is a positive-definite symmetric matrix. Since A is symmetric, A is or-thogonally diagonalizable, so that there is some orthogonal matrix P and diagonal matrix D such thatA = PDP". If we wish to then compute the SVD of A, say A = UEV*, which of the following is trueof the general situation?|3D• We may take E = D, and U = V = P.• We may take E = D, but we may not be able to take U = V = P.• We may take one of U and V to be P, but cannot take both to be P, and we cannot take E= Din general.

We will use the knowledge of standard value decomposition (SVD) of a square matrix.

Suppose that A € Mnxn(R) is a positive-definite symmetric matrix. Since A is symmetric, A is or- thogonally diagonalizable, so that there is some orthogonal matrix P and diagonal matrix D such that A = PDP". If we wish to then compute the SVD of A, say A = of the general situation? UEV*, which of the following is true • We may take E = D, and U = V = P. • We may take E= D, but we may not be able to take U = V = P. • We may take one of U and V to be P, but cannot take both to be P, and we cannot take E = D in general.