Matrix Inequalities for Iterative Systems

Hanjo Taubig

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English

CRC Press
31 March 2021

Algebra; Combinatorics & graph theory; Computing: general

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.

By: Hanjo Taubig
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 254mm, Width: 178mm,
Weight: 408g
ISBN: 9780367782603
ISBN 10: 036778260X
Pages: 218
Publication Date: 31 March 2021
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

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.

Hanjo Taubig