Article
Harnack Type Inequalities for Matrices in Majorization
Linear Algebra and its Applications
Document Type
Article
Publication Date
3-1-2020
Keywords
- Cartesian decomposition,
- Cayley transform,
- Harnack inequality,
- Singular value
Disciplines
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.
Additional Comments
CSC grant #: 201906920042
DOI
10.1016/j.laa.2019.11.025
Citation Information
Chaojun Yang and Fuzhen Zhang. "Harnack Type Inequalities for Matrices in Majorization" Linear Algebra and its Applications Vol. 588 (2020) p. 196 - 209 ISSN: 0024-3795 Available at: http://works.bepress.com/fuzhen-zhang/175/
©2019 Elsevier Inc. All rights reserved.