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.

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