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? 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.

List of contents

Introduction. Notation and Basic Facts. Motivation. Diagonalization and Spectral Decomposition. Undirected Graphs / Hermitian Matrices. General Results. Restricted Graph Classes. Directed Graphs / Nonsymmetric. Walks and Alternating Walks in Directed Graphs. Powers of Row and Column Sums. Applications. Bounds for the Largest Eigenvalue. Iterated Kernels. Conclusion. Bibliography. Index.

About the author

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

Product details

• Authors: Hanjo Taubig, Hanjo (Technische Universitat Munchen Taubig, Taubig Hanjo
• Publisher: Taylor & Francis Ltd.
• Languages: English
• Product format: Paperback / Softback
• Released: 31.05.2021
• EAN: 9780367782603
• ISBN: 978-0-367-78260-3
• No. of pages: 218
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > General, dictionaries; Algebra, SCIENCE / Life Sciences / General, MATHEMATICS / General, MATHEMATICS / Algebra / General, Mathematics, MATHEMATICS / Combinatorics, Combinatorics & graph theory, Information technology: general issues, Information technology: general topics, Combinatorics and graph theory