Advances in matrix inequalities

by Ghaemi, Mohammad Bagher

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Title Statements

Full title :Advances in matrix inequalities / Mohammad Bagher Ghaemi, Nahid Gharakhanlu, Themistocles M. Rassias, Reza Saadati.

Summary

This self-contained monograph unifies theorems, applications and problem solving techniques of matrix inequalities. In addition to the frequent use of methods from Functional Analysis, Operator Theory, Global Analysis, Linear Algebra, Approximations Theory, Difference and Functional Equations and more, the reader will also appreciate techniques of classical analysis and algebraic arguments, as well as combinatorial methods. Subjects such as operator Young inequalities, operator inequalities for positive linear maps, operator inequalities involving operator monotone functions, norm inequalities, inequalities for sector matrices are investigated thoroughly throughout this book which provides an account of a broad collection of classic and recent developments. Detailed proofs for all the main theorems and relevant technical lemmas are presented, therefore interested graduate and advanced undergraduate students will find the book particularly accessible. In addition to several areas of theoretical mathematics, Matrix Analysis is applicable to a broad spectrum of disciplines including operations research, mathematical physics, statistics, economics, and engineering disciplines. It is hoped that graduate students as well as researchers in mathematics, engineering, physics, economics and other interdisciplinary areas will find the combination of current and classical results and operator inequalities presented within this monograph particularly useful.

Edition Statements

Publication Date:2021.

Publication Statements

Publisher(s):Springer
Place of Publication:Cham
Language:eng
Publication Date:2021.

Notes

6.5 Inequalities Involving the Off-Diagonal Block of a PPT Matrix.

The Physical Object

Description:1 online resource (287 pages)

Edition Identifiers

ISBN:9783030760472, 3030760472
DOI:10.1007/978-3-030-76047-2
oclc:on1260343918
LC Classification:QA188
Dewey Decimal:512.9/434

Intro -- Preface -- Contents -- Acronyms -- 1 Elementary Linear Algebra Review -- 1.1 Operators and Matrices in Hilbert Space -- 2 Interpolating the Arithmetic-Geometric Mean Inequality and Its Operator Version -- 2.1 Refinements of the Scalar Young and Heinz Inequalities -- 2.2 Operator Inequalities Involving Improved Young Inequality -- 2.3 Advanced Refinements of the Scalar Reverse Young Inequalities -- 2.4 Improvements of the Operator Reverse Young Inequality -- 3 Operator Inequalities for Positive Linear Maps -- 3.1 On an Operator Kantorovich Inequality for Positive Linear Maps

3.2 A Schwarz Inequality for Positive Linear Maps -- 3.3 Squaring the Reverse Arithmetic-Geometric Mean Inequality -- 3.4 Reverses of Ando's Inequality for Positive Linear Maps -- 3.5 Squaring the Reverse Ando's Operator Inequality -- 4 Operator Inequalities Involving Operator Monotone Functions -- 4.1 Young Inequalities Involving Operator Monotone Functions -- 4.2 Eigenvalue Inequalities Involving Operator Concave Functions -- 4.3 Operator Aczél Inequality Involving Operator Monotone Functions -- 4.4 Norm Inequalities Involving Operator Monotone Functions -- 5 Inequalities for Sector Matrices

5.1 Ha…