----- Find the (real) vectors U,V whose outer product makes the (real) matrix; i.e., U' V = M Clearly, for any real alpha, (U/alpha)' (alpha*V) = M so the vectors are determined only up to a single constant factor. ----- I'm probably missing the obvious, but I wondered about that. It's true that Henry is starting from the assumption that there exists a solution. But instead: Suppose we want to try to solve for x, y, z, w the equation (A B) (x y)' (z w) = ( ) (C D) I.e., the four equations xz = A, xw = B, yz = C, yw = D for randomly chosen A, B, C, D (real or complex). When does there exist a solution? And what about the general case in higher dimensions: Let v, w be unknown vectors in K^n (K = R or C) with v' w = M, an arbitrary n x n matrix of constants in K. When does there exist a solution for v and w ??? —Dan