On the Schur product ofH-matrices and non-negative matrices, and related inequalities
M. Stuart Lynn · Mathematical Proceedings of the Cambridge Philosophical Society · 1964
1.Introduction. Let ℛndenote the set of alln×nmatrices with real elements, and let denote the subset of ℛnconsisting of all real,n×n, symmetric positive-definite matrices. We shall use the notation to denote that minor of the matrixA= (aij) ∈ ℛnwhich is the determinant of the matrix TheSchur Product(Schur (14)) of two matricesA, B∈ ℛnis denned by whereA= (aij),B= (bij),C= (cij) and Let ϕ be the mapping of ℛninto the real line defined by for allA∈ ℛn, where, as in the sequel, .