Matrix Inequalities

Xingzhi Zhan

116 pages, parution le 04/09/2002

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Résumé

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.

Contents

1. Inequalities in the Löwner Partial Order

1.1 The Löwner -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 Semi-definite 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 H šolder 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

L'auteur - Xingzhi Zhan

Zhan, X., Peking University, Beijing, China

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Xingzhi Zhan
Parution	04/09/2002
Nb. de pages	116
Format	15,5 x 23,5
Couverture	Broché
Poids	230g
Intérieur	Noir et Blanc
EAN13	9783540437987