Abstract
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.
| Original language | American English |
|---|---|
| Pages (from-to) | 196-209 |
| Number of pages | 14 |
| Journal | Linear Algebra and its Applications |
| Volume | 588 |
| State | Published - Mar 1 2020 |
Bibliographical note
Publisher Copyright:© 2019 Elsevier Inc.
Funding
This work was done when Chaojun Yang was a CSC(201906920042)-sponsored Ph.D. student at Nova Southeastern University during the 2019-2020 academic year. The authors thank Prof. Zhaolin Jiang for initiating the work and Prof. Lei Cao for discussions.
| Funders | Funder number |
|---|---|
| Nova Southeastern University | |
| China Scholarship Council | 201906920042 |
ASJC Scopus Subject Areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics
Keywords
- Cartesian decomposition
- Cayley transform
- Harnack inequality
- Singular value
Disciplines
- Mathematics
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