Inequalities involving Hadamard products of positive semidefinite matrices
type: Item
instance of: scholarly article
title: Inequalities involving Hadamard products of positive semidefinite matrices
zbMATH Open document ID: 0949.15026
author: Shuangzhe Liu
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-12-05T00:00:00Z
review text: This paper is an extension of two inequalities. An inequality established by \textit{G. P. H. Styan} [Linear Algebra Appl. 6, 217-240 (1973; Zbl 0255.15002)] is on the Hadamard product and a correlation matrix. An inequality obtained by \textit{B. Wang} and \textit{F. Zhang} [Linear Multilinear Algebra 43, No. 1-3, 315-326 (1997; Zbl 0893.15008)] involves the Hadamard product and Schur complements. These two inequalities hold in the positive definite matrix case. Based on Albert's theorem, the author presents their extensions to cover the positive semidefinite matrix case. The relevant inequalities are also given. The main results are in Section 2.
Mathematics Subject Classification ID: 15A45
zbMATH DE Number: 1439374
zbMATH Keywords: Hadamard product
zbMATH Keywords: correlation matrix
zbMATH Keywords: Schur complements
zbMATH Keywords: Albert's theorem
zbMATH Keywords: positive semidefinite matrix
zbMATH Keywords: inequalities
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
full work available at URL: jmaa.1999.6670
OpenAlex ID: W1969061789
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DOI: 10.1006/JMAA.1999.6670
description: scientific article; zbMATH DE number 1439374