Matrix Inequalities / by Xingzhi Zhan.

Format:

Book

Author/Creator:

Zhan, Xingzhi, 1965- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1790.

Lecture Notes in Mathematics, 0075-8434 ; 1790

Language:

English

Subjects (All):

Algebra.

Matrices.

Operator theory.

Linear and Multilinear Algebras, Matrix Theory.

Operator Theory.

Local Subjects:

Algebra.

Linear and Multilinear Algebras, Matrix Theory.

Operator Theory.

Physical Description:

1 online resource (VIII, 124 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.

System Details:

text file PDF

Summary:

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:

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.

Other Format:

Printed edition:

ISBN:

9783540454212

Access Restriction:

Restricted for use by site license.