Harnack type inequalities for matrices in majorization

被引：1
作者：
Yang, Chaojun [1 ]
Zhang, Fuzhen [2 ]
机构：
[1] Suzhou Univ, Dept Math, Suzhou, Peoples R China
[2] Nova Southeastern Univ, Dept Math, Ft Lauderdale, FL 33314 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2020年 / 588卷
关键词：
Cartesian decomposition; Cayley transform; Harnack inequality; Singular value;
D O I：
10.1016/j.laa.2019.11.025
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Following the recent work of Jiang and Lin (2020) [12], 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) [19]; 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. (C) 2019 Elsevier Inc. All rights reserved.
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页码：196 / 209
页数：14
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