Matrix inequalities for iterative systems
The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequa…
Read More ↓Title Statements
- Full title :Matrix inequalities for iterative systems / by Hanjo Taubig.
Summary
The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.
Read More ↓Edition Statements
- Publication Date:©2016
- Edition:First edition
Publication Statements
- Publisher(s):CRC Press
- Place of Publication:Boca Raton, FL
- Language:eng
- Publication Date:©2016
The Physical Object
- Description:1 online resource (218 pages) : : 3 illustrations
Edition Identifiers
- ISBN:9781315166131, 1315166135, 9781351679084, 1351679082, 9781498777797, 1498777791, 9781498777773, 1498777775
- DOI:10.1201/9781315166131
- oclc:on1069711649
- LC Classification:QA188
- Dewey Decimal:512.9/434
Table of Contents
Part INTRODUCTION -- chapter 1 Notation and Basic Facts -- chapter 2 Motivation -- chapter 3 Diagonalization and Spectral Decomposition -- part UNDIRECTED GRAPHS / HERMITIAN MATRICES -- chapter 4 General Results -- chapter 5 Restricted Graph Classes -- part DIRECTED GRAPHS / NONSYMMETRIC MATRICES -- chapter 6 Walks and Alternating Walks in Directed Graphs -- chapter 7 Powers of Row and Column Sums -- part APPLICATIONS -- chapter 8 Bounds for the Largest Eigenvalue -- chapter 9 Iterated Kernels.
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