Springer Advances in Matrix Inequalities: 176 (Springer Optimization and Its Applications, 176)

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. From the Back Cover 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. About the Author Mohammad Bagher Ghaemi is an associate professor of mathematics at the Iran University of Science and Technology, Tehran. His research interests include operator theory, nonlinear analysis, approximation theory, functional analysis, functional equations, inequalities and applications. Professor Ghaemi received his PhD in mathematics from Glasgow University, Scotland, in 2000; his PhD advisor was P.G. Spain. He has published more than 60 papers. Nahid Gharakhanlu received her PhD in pure mathematics from the Iran University of Science and Technology, Tehran in 2017.  Her PhD advisor was Mohammad Bagher Ghaemi. Her research interests include matrix analysis, functional analysis, operator theory, linear algebra, inequalities and their applications. Themistocles M. Rassias is professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional