Inequalities Involving the Inverses of Positive Definite Matrices

Abstract

Let G be a permutation group of degree m. Let x be an irreducible complex character of G. If A = (aij) is an m-square matrix, the generalised matrix function of A based on G and x is defined byFor example if G = Sm, the full symmetric group, and x is the alternating character, then d = determinant. If G = Sm and x is identically 1, then d = permanent.