Matrix and Operator Equations and Applications

Mohammad Sal Moslehian

ISBN 10: 303125385X / ISBN 13: 9783031253850

Published by Springer Nature Switzerland, Springer Nature Switzerland Jul 2023, 2023

About this Item

Neuware -This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way. The main aim of this contributed book is to study several important matrix and operator equalities and equations in a systematic and self-contained fashion. Some powerful methods have been used to investigate some significant equations in functional analysis, operator theory, matrix analysis, and numerous subjects in the last decades.The book is divided into two parts: (I) Matrix Equations and (II) Operator Equations.In the first part, the state-of-the-art of systems of matrix equations is given and generalized inverses are used to find their solutions. The semi-tensor product of matrices is used to solve quaternion matrix equations. The contents of some chapters are related to the relationship between matrix inequalities, matrix means, numerical range, and matrix equations. In addition, quaternion algebras and their applications are employed in solving some famous matrix equations like Sylvester, Stein, and Lyapunov equations. A chapter devoted to studying Hermitian polynomial matrix equations, which frequently arise from linear-quadratic control problems. Moreover, some classical and recently discovered inequalities for matrix exponentials are reviewed.In the second part, the latest developments in solving several equations appearing in modern operator theory are demonstrated. These are of interest to a wide audience of pure and applied mathematicians. For example, the Daugavet equation in the linear and nonlinear setting, iterative processes and Volterra-Fredholm integral equations, semicircular elements induced by connected finite graphs, free probability, singular integral operators with shifts, and operator differential equations closely related to the properties of the coefficient operators in some equations are discussed.The chapters give acomprehensive account of their subjects. The exhibited chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 776 pp. Englisch.

Seller Inventory # 9783031253850

Bibliographic Details

• Title: Matrix and Operator Equations and Applications
• Publisher: Springer Nature Switzerland, Springer Nature Switzerland Jul 2023
• Publication Date: 2023
• Language: English
• ISBN 10: 303125385X
• ISBN 13: 9783031253850
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 45D millimeters 241 millimeters width by 160 millimeters height by 45 millimeters depth
• Weight: 1455 grams

About this title

Synopsis

This book concerns matrix and operator equations that are widely applied in various disciplines of science to formulate challenging problems and solve them in a faithful way. The main aim of this contributed book is to study several important matrix and operator equalities and equations in a systematic and self-contained fashion. Some powerful methods have been used to investigate some significant equations in functional analysis, operator theory, matrix analysis, and numerous subjects in the last decades.

The book is divided into two parts: (I) Matrix Equations and (II) Operator Equations.

In the first part, the state-of-the-art of systems of matrix equations is given and generalized inverses are used to find their solutions. The semi-tensor product of matrices is used to solve quaternion matrix equations. The contents of some chapters are related to the relationship between matrix inequalities, matrix means, numerical range, and matrix equations. In addition, quaternion algebras and their applications are employed in solving some famous matrix equations like Sylvester, Stein, and Lyapunov equations. A chapter devoted to studying Hermitian polynomial matrix equations, which frequently arise from linear-quadratic control problems. Moreover, some classical and recently discovered inequalities for matrix exponentials are reviewed.

In the second part, the latest developments in solving several equations appearing in modern operator theory are demonstrated. These are of interest to a wide audience of pure and applied mathematicians. For example, the Daugavet equation in the linear and nonlinear setting, iterative processes and Volterra-Fredholm integral equations, semicircular elements induced by connected finite graphs, free probability, singular integral operators with shifts, and operator differential equations closely related to the properties of the coefficient operators in some equations are discussed.

The chapters give acomprehensive account of their subjects. The exhibited chapters are written in a reader-friendly style and can be read independently. Each chapter contains a rich bibliography. This book is intended for use by both researchers and graduate students of mathematics, physics, and engineering.

About the Author

M. S. Moslehian is a Professor of Mathematics at the Ferdowsi University of Mashhad, a member of the academy of sciences of Iran, and the President of Iran. Math. Soc. His research concerns operator theory and matrix analysis. He was a Senior Associate in ICTP (Italy) and a visiting professor at several universities around the world. He is the editor-in-chief of the journals "Banach J. Math. Anal.", "Ann. Funct. Anal.", and "Adv. Oper. Theory" being published by Birkhäuser/Springer.