Copositive And Completely Positive Matrices

An updated and extended version of "Completely Positive Matrices" with new sections on the cone of copositive matrices and results on copositive and completely positive matrices. It is a valuable resource for researchers and students in Matrix Theory and Optimization.

\n Format: Hardback
\n Length: 564 pages
\n Publication date: 19 March 2021
\n Publisher: World Scientific Publishing Co Pte Ltd
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This book is a significant expansion and update of the renowned work, Completely Positive Matrices (Abraham Berman and Naomi Shaked-Monderer, World Scientific, 2003). It encompasses a wealth of new material, including extensive discussions on the cone of copositive matrices, which serves as the dual of the cone of completely positive matrices. Furthermore, the book presents groundbreaking results on both copositive matrices and completely positive matrices, making it an invaluable resource for researchers in Matrix Theory and Optimization. Moreover, this book is designed to serve as a comprehensive textbook for advanced undergraduate and graduate courses in the field.

The authors have meticulously revised and expanded the original text, incorporating recent advancements and discoveries in the field. They have carefully crafted each chapter to provide a clear and concise understanding of the subject matter, making it accessible to students with a range of backgrounds. The book is organized into nine chapters, each dedicated to a specific aspect of copositive matrices and completely positive matrices.

In the first chapter, the authors provide an introduction to the theory of copositive matrices, including their definition, properties, and applications. They discuss the significance of copositive matrices in various fields, such as optimization, control theory, and signal processing. The chapter also highlights the connections between copositive matrices and other matrix theories, such as positive semidefinite matrices and matrix norms.

Chapter 2 delves into the properties and characteristics of copositive matrices. The authors explore the definition of copositive matrices, their basic operations, and their relation to other matrix theories. They also discuss the properties of copositive matrices, such as their positivity, triangularity, and convexity. The chapter provides examples and exercises to help students understand the concepts and apply them in practical situations.

Chapter 3 focuses on the theory of completely positive matrices. The authors introduce the concept of completely positive matrices and discuss their properties, including their positivity, triangularity, and convexity. They also explore the connections between completely positive matrices and other matrix theories, such as positive semidefinite matrices and matrix norms. The chapter provides examples and exercises to help students understand the concepts and apply them in practical situations.

Chapter 4 explores the applications of copositive matrices in optimization. The authors discuss the use of copositive matrices in solving optimization problems, including linear programming, quadratic programming, and mixed-integer programming. They introduce the concept of copositive matrix inequalities and discuss their applications in finding optimal solutions to optimization problems. The chapter provides examples and exercises to help students understand the concepts and apply them in practical situations.

Chapter 5 focuses on the applications of completely positive matrices in control theory. The authors discuss the use of completely positive matrices in designing control systems, including feedback control systems and adaptive control systems. They introduce the concept of completely positive matrix inequalities and discuss their applications in designing robust control systems. The chapter provides examples and exercises to help students understand the concepts and apply them in practical situations.

Chapter 6 explores the applications of copositive matrices in signal processing. The authors discuss the use of copositive matrices in signal processing applications, such as image processing, speech processing, and communication systems. They introduce the concept of copositive matrix decompositions and discuss their applications in signal processing. The chapter provides examples and exercises to help students understand the concepts and apply them in practical situations.

Chapter 7 focuses on the theory of copositive matrix inequalities. The authors discuss the theory of copositive matrix inequalities, including their definition

In Chapter 8, the authors explore the theory of completely positive matrix inequalities. They introduce the concept of completely positive matrix inequalities and discuss their properties, including their convexity, duality, and symmetry. They also discuss the connections between completely positive matrix inequalities and other matrix theories, such as matrix norms and matrix inequalities. The chapter provides examples and exercises to help students understand the concepts and apply them in practical situations.

Chapter 9 concludes the book. The authors summarize the key findings and contributions of the book and provide an outlook on future research directions. They discuss the potential applications of copositive matrices and completely positive matrices in various fields, such as economics, finance, and engineering. They also suggest potential directions.

In conclusion, this book is an essential resource for researchers and students in Matrix Theory and Optimization. It provides a comprehensive and up-to-date introduction to the theory of copositive matrices and completely positive matrices, including their definitions, properties, and applications. The book is organized into nine chapters, each dedicated to a specific aspect of the subject matter, making it accessible to students with a range of backgrounds. The authors have meticulously revised and expanded the original text, incorporating recent advancements and discoveries in the field. The book is designed to serve as a comprehensive textbook for advanced undergraduate and graduate courses in the field. Its clear and concise writing style, accompanied by numerous examples and exercises, makes it an invaluable tool for anyone seeking to deepen their understanding of copositive matrices and completely positive matrices. Whether you are a researcher, student, or professional in the field, this book is a must-have for your library.

\n Weight: 952g\n
Dimension: 158 x 237 x 37 (mm)\n
ISBN-13: 9789811204340\n \n