On the Schur product ofH-matrices and non-negative matrices, and related inequalities

Abstract

1.Introduction. Let ℛndenote the set of alln×nmatrices with real elements, and letdenote the subset of ℛnconsisting of all real,n×n, symmetric positive-definite matrices. We shall use the notationto denote that minor of the matrixA= (aij) ∈ ℛnwhich is the determinant of the matrixTheSchur Product(Schur (14)) of two matricesA, B∈ ℛnis denned bywhereA= (aij),B= (bij),C= (cij) andLet ϕ be the mapping of ℛninto the real line defined byfor allA∈ ℛn, where, as in the sequel,.