Matrix Inequalities / Edition 1

by Xingzhi Zhan

Overview

The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.

Product Details

ISBN-13:	9783540437987
Publisher:	Springer Berlin Heidelberg
Publication date:	09/24/2002
Series:	Lecture Notes in Mathematics , #1790
Edition description:	2002
Pages:	124
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Inequalities in the Loewner Partial Order: The Loewner-Heinz inequality; Maps on matrix spaces; Inequalities for matrix powers; Block matrix techniques.- Majorization and Eigenvalues: Majorizations; Eigenvalues of Hadamard products; Singular Values: Matrix Young inequalities; Singular values of Hadamard products; Differences of positive semidefinite matrices; Matrix Cartesian decompositions; Singular values and matrix entries.- Norm Inequalities: Operator monotone functions; Cartesian decompositions revisited; Arithmetic-geometric mean inequalities; Inequalities of Holder and Minkowski types; Permutations of matrix entries; The numerical radius; Norm estimates of banded matrices.- Solution of the van der Waerden Conjecture.