Refinements of the Schur inequality for principal characters

Abstract

Let G be a subgroup of S n . For any n-square complex matrix A = [ a ij ], define d G(A) = Sum; σϵG Π i=1 n a iσ(i) For this matrix function the Schur inequality asserts that d C ( A) ≥ det A if A is positive definite. This article contains a result which refines the above inequality and improves on some results of Bapat, Bunce, and Marcus and Sandy.