Matrix Inequalities for Iterative Systems

Hanjo Taubig

November 18, 2016 by CRC Press
Reference - 218 Pages - 3 B/W Illustrations
ISBN 9781498777773 - CAT# K29783

USD$179.95

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Features

  • Provides the first systematic study / survey on inequalities for entry sums of matrix powers.
  • Discusses the known results and explains how they are related.
  • Unifies the known inequalities and shows many new and more general results.
  • Attaches importance to elementary proofs that are easy to follow, even by undergraduate students.

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.