Overview
- Suitable for both researchers and graduate students with a basic knowledge of operator theory
- Includes the latest developments in matrix and operator equations
- Contains contributions by a number of specialists
Part of the book series: Mathematics Online First Collections (MOFC)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (17 chapters)
-
Front Matter
-
Matrix Equations
-
Front Matter
-
-
Operator Equations
-
Front Matter
-
Keywords
- Operator equation
- Matrix equation
- Split quaternion
- Differential equation
- Numerical range
- Matrix quadratic equation
- Log-majorization
- Generalized inverse
- Operator mean
- Berezin number
- Reproducing kernel Hilbert space
- Singular integral operator with shifts
- Graph groupoids
- Quaternion matrix equation
- Yang-Baxter-like matrix equation
- Sylvester equation
- Matrix polynomial equation
- Variational problem
- Daugaet equation
- Volterra-Fredholm integral equation
About this book
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.
Editors and Affiliations
About the editor
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.
Bibliographic Information
Book Title: Matrix and Operator Equations and Applications
Editors: Mohammad Sal Moslehian
Series Title: Mathematics Online First Collections
DOI: https://doi.org/10.1007/978-3-031-25386-7
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-25385-0Published: 30 July 2023
Softcover ISBN: 978-3-031-25388-1Due: 30 August 2023
eBook ISBN: 978-3-031-25386-7Published: 29 July 2023
Series ISSN: 2730-633X
Series E-ISSN: 2730-6348
Edition Number: 1
Number of Pages: X, 765
Number of Illustrations: 10 b/w illustrations
Topics: Operator Theory