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.
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.
Publication Statements
- Publisher(s):CRC Press
- Place of Publication:Portland
- Language:eng
- Publication Date:2016.
Notes
4.4.5 The Method of Expectation of Random Variables.
The Physical Object
- Description:1 online resource (219 pages)
Edition Identifiers
- ISBN:9781351679091, 1351679090, 9781498777797, 1498777791, 9781498777773, 1498777775
- oclc:ocn972291541
- LC Classification:QA188.T36 2017
- Dewey Decimal:512.9434
Table of Contents
Cover; Half Title; Title Page; Copyright Page; Dedication; Acknowledgments; Preface; Table of Contents; Symbol Description; I: INTRODUCTION; 1: Notation and Basic Facts; 1.1 Matrices and Vectors; 1.1.1 Matrices; 1.1.2 Vectors; 1.1.3 Matrix Classes; 1.2 Graphs; 1.2.1 Degrees; 1.2.2 Adjacency Matrix; 1.3 Number of Walks in Graphs; 1.3.1 Walks; 1.3.2 Number of Walks; 1.4 Entry Sums and Matrix Powers; 1.4.1 Entry Sums of Matrix Powers; 1.4.2 Number of Walks and Matrix Powers; 1.4.3 Local Decomposition; 1.5 Subsets, Submatrices, and Weighted Entry Sums; 1.5.1 Selected Walks and Submatrices.
1.5.2 Weighted Entry Sums1.5.3 Quadratic Forms and Hermitian Matrices; 1.5.4 Global Decomposition; 1.6 Elementary Inequalities for Vectors and Sequences; 1.6.1 The Inequalities of Cauchy, Bunyakovsky, and Schwarz; 1.6.2 The Inequalities of Rogers and Hölder; 1.6.3 Chebyshev's Sum Inequality; 1.6.4 Inequalities for Arithmetic, Geometric, Harmonic, and Power Means; 2: Motivation; 2.1 Simple Combinatorial Problems; 2.2 Automata and Formal Languages; 2.3 Graph Density, Maximum Clique and Densest k-Subgraph; 2.4 The Number of Paths and Extremal Graph Theory; 2.5 Means, Variances, and Irregularity.
2.6 …
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