Inequalities involving Hadamard products of positive semidefinite matrices

Shuangzhe Liu

doi:10.1006/jmaa.1999.6670

Inequalities involving Hadamard products of positive semidefinite matrices

Shuangzhe Liu

Research output: Contribution to journal › Article › peer-review

11 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 language	English
Pages (from-to)	458-463
Number of pages	6
Journal	Journal of Mathematical Analysis and Applications
Volume	243
Issue number	2
DOIs	https://doi.org/10.1006/jmaa.1999.6670
Publication status	Published - 15 Mar 2000
Externally published	Yes

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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",

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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

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DO - 10.1006/jmaa.1999.6670

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EP - 463

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Inequalities involving Hadamard products of positive semidefinite matrices

Abstract

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