A sufficient condition for the monotonicity of a positive definite matrix
type: Item
instance of: scholarly article
title: A sufficient condition for the monotonicity of a positive definite matrix
zbMATH Open document ID: 1024.15009
published in: Computational Mathematics and Mathematical Physics
publication date: 2003-06-29T00:00:00Z
review text: The author considers the set of real matrices \(M_n\) of order \(n\geq{2}\) and \(M_n^+\subset{M_n}\) the set of real symmetric positive definite matrices. Monotonicity of a matrix \(A\in{M_n^+}\) (i.e., \(A\) is nonsingular and all entries in \(A^{-1}\) are nonnegative) is proved under the condition that all of its principal submatrices of a fixed order are monotone.
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 1940598
zbMATH Keywords: positive definite matrix
zbMATH Keywords: monotonicity
zbMATH Keywords: nonsingular principal submatrix
author: A. V. Gavrilov
reviewed by: A. Tret'yakov
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1940598