Inequalities involving Hadamard products of positive semidefinite matrices

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

An inequality established by G. P. H. Styan (1973, Linear Algebra Appl.,6, 217-240) is on the Hadamard product and a correlation matrix. An inequality obtained by B.-Y. Wang and F. Zhang (1997, Linear and Multilinear Algebra, 43, 315-326) involves the Hadamard product and Schur complements. These two inequalities hold in the positive definite matrix case. Based on Albert's theorem, we present their extensions to cover the positive semidefinite matrix case. We also give relevant inequalities.

Original languageEnglish
Pages (from-to)458-463
Number of pages6
JournalJournal of Mathematical Analysis and Applications
Volume243
Issue number2
DOIs
Publication statusPublished - 15 Mar 2000
Externally publishedYes

Fingerprint

Hadamard Product
Positive Semidefinite Matrix
Linear algebra
Multilinear Algebra
Algebra
Schur Complement
Positive definite matrix
Correlation Matrix
Cover
Theorem

Cite this

@article{8d12596aacd24c57a913620a04bef62e,
title = "Inequalities involving Hadamard products of positive semidefinite matrices",
abstract = "An inequality established by G. P. H. Styan (1973, Linear Algebra Appl.,6, 217-240) is on the Hadamard product and a correlation matrix. An inequality obtained by B.-Y. Wang and F. Zhang (1997, Linear and Multilinear Algebra, 43, 315-326) involves the Hadamard product and Schur complements. These two inequalities hold in the positive definite matrix case. Based on Albert's theorem, we present their extensions to cover the positive semidefinite matrix case. We also give relevant inequalities.",
keywords = "Albert's theorem, Correlation matrix, Hadamard product, Khatri-Rao product, Kronecker product, Schur complements",
author = "Shuangzhe Liu",
year = "2000",
month = "3",
day = "15",
doi = "10.1006/jmaa.1999.6670",
language = "English",
volume = "243",
pages = "458--463",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press Inc.",
number = "2",

}

Inequalities involving Hadamard products of positive semidefinite matrices. / Liu, Shuangzhe.

In: Journal of Mathematical Analysis and Applications, Vol. 243, No. 2, 15.03.2000, p. 458-463.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Inequalities involving Hadamard products of positive semidefinite matrices

AU - Liu, Shuangzhe

PY - 2000/3/15

Y1 - 2000/3/15

N2 - An inequality established by G. P. H. Styan (1973, Linear Algebra Appl.,6, 217-240) is on the Hadamard product and a correlation matrix. An inequality obtained by B.-Y. Wang and F. Zhang (1997, Linear and Multilinear Algebra, 43, 315-326) involves the Hadamard product and Schur complements. These two inequalities hold in the positive definite matrix case. Based on Albert's theorem, we present their extensions to cover the positive semidefinite matrix case. We also give relevant inequalities.

AB - An inequality established by G. P. H. Styan (1973, Linear Algebra Appl.,6, 217-240) is on the Hadamard product and a correlation matrix. An inequality obtained by B.-Y. Wang and F. Zhang (1997, Linear and Multilinear Algebra, 43, 315-326) involves the Hadamard product and Schur complements. These two inequalities hold in the positive definite matrix case. Based on Albert's theorem, we present their extensions to cover the positive semidefinite matrix case. We also give relevant inequalities.

KW - Albert's theorem

KW - Correlation matrix

KW - Hadamard product

KW - Khatri-Rao product

KW - Kronecker product

KW - Schur complements

UR - http://www.scopus.com/inward/record.url?scp=0034652896&partnerID=8YFLogxK

U2 - 10.1006/jmaa.1999.6670

DO - 10.1006/jmaa.1999.6670

M3 - Article

VL - 243

SP - 458

EP - 463

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -