Mathematics Faculty Articles

Title

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

Document Type

Article

Publication Date

3-1-2009

Publication Title

Linear Algebra and its Applications

Keywords

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

ISSN

0024-3795

Volume

430

Issue/No.

5-6

First Page

1499

Last Page

1508

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

Comments

Under an Elsevier user license

AMS classification

  • 15A15;
  • 15A24;
  • 15A45

DOI

10.1016/j.laa.2007.11.011