Mathematics Faculty Articles

Harnack Type Inequalities for Matrices in Majorization

Document Type

Article

Publication Date

3-1-2020

Publication Title

Linear Algebra and its Applications

Keywords

Cartesian decomposition, Cayley transform, Harnack inequality, Singular value

ISSN

0024-3795

Volume

588

First Page

196

Last Page

209

Abstract

Following the recent work of Jiang and Lin (2020), we present more results (bounds) on Harnack type inequalities for matrices in terms of majorization (i.e., in partial products) of eigenvalues and singular values. We discuss and compare the bounds derived through different ways. Jiang and Lin's results imply Tung's version of Harnack's inequality (1964); our results are stronger and more general than Jiang and Lin's. We also show some majorization inequalities concerning Cayley transforms. Some open problems on spectral norm and eigenvalues are proposed.

Comments

©2019 Elsevier Inc. All rights reserved.

Additional Comments

CSC grant #: 201906920042

DOI

10.1016/j.laa.2019.11.025

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Peer Reviewed

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