Matrix Inequalities

ISBN-13: 9783540437987 / Angielski / Miękka / 2002 / 124 str.

Yorck Sommerhauser; Xingzhi Zhan

Opis

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.

Spis treści

1. Inequalities in the Loewner Partial Order 1.1 The Loewner-Heinz inequality 1.2 Maps on matrix spaces 1.3 Inequalities for matrix powers 1.4 Block matrix techniques 2. Majorization and Eigenvalues 2.1 Majorizations 2.2 Eigenvalues of Hadamard products 3. Singular Values 3.1 Matrix Young inequalities 3.2 Singular values of Hadamard products 3.3 Differences of positive semidefinite matrices 3.4 Matrix Cartesian decompositions 3.5 Singular values and matrix entries 4. Norm Inequalities 4.1 Operator monotone functions 4.2 Cartesian decompositions revisited 4.3 Arithmetic-geometric mean inequalities 4.4 Inequalities of Holder and Minkowski types 4.5 Permutations of matrix entries 4.6 The numerical radius 4.7 Norm estimates of banded matrices 5. Solution of the van der Waerden Conjecture