A reverse Hadamard inequality Original Research Article

Let U be an n × n unitary matrix with determinant equal to 1. Let A be an n × n real matrix with rank(A) less-than-or-equals, slant 2 and entries satisfying aij greater-or-equal, slanted 1 for 1 less-than-or-equals, slant i, j less-than-or-equals, slant n. Then it follows that det(A ring operator U) greater-or-equal, slanted 1. This reversal of the Hadamard inequality can be obtained easily from an old result of Fiedler. In this article we present a different proof of this fact and discuss its ramifications.