A REVERSE HADAMARD INEQUALITY

Let U be an n x n unitary matrix with determinant equal to 1. Let A be an n x n real matrix with rank(A) less than or equal to 2 and entries satisfying a(ij) greater than or equal to 1 for 1 less than or equal to i, j less than or equal to n. Then it follows that det(A circle U) greater than or equal to 1. This reversal of the Hadamard inequality c an be obtained easily from an old result of Fiedler. In this article w e present a different proof of this fact and discuss its ramifications .