Revisiting Hua-Marcus-Bellman-Ando Inequalities on Contractive Matrices

Changqing Xu; Zhaodi Xu; Fuzhen Zhang

doi:10.1016/j.laa.2007.11.011

Revisiting Hua-Marcus-Bellman-Ando Inequalities on Contractive Matrices

Changqing Xu
, Zhaodi Xu
, Fuzhen Zhang

Department of Mathematics

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

10 Scopus citations

Abstract

Loo-Keng Hua showed some elegant matrix and determinant inequalities via a matrix identity and proved the positive semidefiniteness of a matrix involving the determinants of contractive matrices through group representation theory. His study was followed by M. Marcus, R. Bellman and T. Ando. The purpose of current paper is to revisit the Hua's original work and the results of Marcus, Bellman and Ando with our comments, and to present analogs and extensions to their results. © 2007 Elsevier Inc. All rights reserved.

Original language	American English
Pages (from-to)	1499-1508
Number of pages	10
Journal	Linear Algebra and its Applications
Volume	430
Issue number	5-6
DOIs	https://doi.org/10.1016/j.laa.2007.11.011
State	Published - Mar 1 2009

Funding

Keywords: Contractions; Contractive matrices; Determinantal inequalities; Hua’s determinant inequality; Hua’s matrix inequality; Matrix inequalities; Schur complements ∗ Corresponding author. E-mail addresses: [email protected] (C. Xu), [email protected] (Z. Xu), [email protected] (F. Zhang). 1Work of this author was supported in part by the Fund for the International Cooperation from the International Department of Zhejiang Province. 2 Work of this author was supported in part by NSU President’s Faculty Research and Development Grant 2007-2008 with Co-PIs G.P.H. Styan and J. Novak.

Funders
International Department of Zhejiang Province
Namseoul University

ASJC Scopus Subject Areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

Keywords

Contractions
Contractive matrices
Determinantal inequalities
Hua's determinant
Hua's matrix inequality
Inequality
Matrix inequalities
Schur complements
Hua's determinant inequality

Disciplines

Mathematics

Access to Document

10.1016/j.laa.2007.11.011

http://www.sciencedirect.com/science/article/pii/S0024379507005307

Cite this

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title = "Revisiting Hua-Marcus-Bellman-Ando Inequalities on Contractive Matrices",

abstract = "Loo-Keng Hua showed some elegant matrix and determinant inequalities via a matrix identity and proved the positive semidefiniteness of a matrix involving the determinants of contractive matrices through group representation theory. His study was followed by M. Marcus, R. Bellman and T. Ando. The purpose of current paper is to revisit the Hua's original work and the results of Marcus, Bellman and Ando with our comments, and to present analogs and extensions to their results. {\textcopyright} 2007 Elsevier Inc. All rights reserved.",

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author = "Changqing Xu and Zhaodi Xu and Fuzhen Zhang",

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T1 - Revisiting Hua-Marcus-Bellman-Ando Inequalities on Contractive Matrices

AU - Xu, Changqing

AU - Xu, Zhaodi

AU - Zhang, Fuzhen

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Y1 - 2009/3/1

N2 - Loo-Keng Hua showed some elegant matrix and determinant inequalities via a matrix identity and proved the positive semidefiniteness of a matrix involving the determinants of contractive matrices through group representation theory. His study was followed by M. Marcus, R. Bellman and T. Ando. The purpose of current paper is to revisit the Hua's original work and the results of Marcus, Bellman and Ando with our comments, and to present analogs and extensions to their results. © 2007 Elsevier Inc. All rights reserved.

AB - Loo-Keng Hua showed some elegant matrix and determinant inequalities via a matrix identity and proved the positive semidefiniteness of a matrix involving the determinants of contractive matrices through group representation theory. His study was followed by M. Marcus, R. Bellman and T. Ando. The purpose of current paper is to revisit the Hua's original work and the results of Marcus, Bellman and Ando with our comments, and to present analogs and extensions to their results. © 2007 Elsevier Inc. All rights reserved.

KW - Contractions

KW - Contractive matrices

KW - Determinantal inequalities

KW - Hua's determinant

KW - Hua's matrix inequality

KW - Inequality

KW - Matrix inequalities

KW - Schur complements

KW - Hua's determinant inequality

UR - https://nsuworks.nova.edu/math_facarticles/102

UR - http://www.sciencedirect.com/science/article/pii/S0024379507005307

UR - https://www.scopus.com/pages/publications/58349089079

UR - https://www.scopus.com/pages/publications/58349089079#tab=citedBy

U2 - 10.1016/j.laa.2007.11.011

DO - 10.1016/j.laa.2007.11.011

M3 - Article

SN - 0024-3795

VL - 430

SP - 1499

EP - 1508

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

IS - 5-6

ER -

Revisiting Hua-Marcus-Bellman-Ando Inequalities on Contractive Matrices

Abstract

Funding

ASJC Scopus Subject Areas

Keywords

Disciplines

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