Linear Algebra Ii: Advanced Topics For Applications

The second volume of the University of Tokyo (UTokyo) Engineering Course linear algebra book covers various topics such as matrices and graphs, nonnegative matrices, systems of linear inequalities, integer matrices, polynomial matrices, generalized inverses, and group representation theory, with independent chapters that can be read in any order.

Format: Paperback / softback
Length: 276 pages
Publication date: 02 September 2022
Publisher: World Scientific Publishing Co Pte Ltd

This is the second volume of a two-volume book on linear algebra in the University of Tokyo (UTokyo) Engineering Course. The objective of this second volume is to branch out from the standard mathematical results presented in the first volume and illustrate useful specific topics pertaining to engineering applications. While linear algebra is primarily concerned with systems of equations and eigenvalue problems for matrices and vectors with real or complex entries, this volume covers other topics such as matrices and graphs, nonnegative matrices, systems of linear inequalities, integer matrices, polynomial matrices, generalized inverses, and group representation theory. The chapters are, for the most part, independent of each other, and can be read in any order according to the reader's interest.

The main objective of this book is to present the mathematical aspects of linear algebraic methods for engineering that will potentially be effective in various application areas.

This book is intended for students in engineering, mathematics, and science who require a solid foundation in linear algebra for their studies. It is also suitable for researchers and practitioners who want to apply linear algebraic methods to solve real-world problems.

The book is organized into five chapters. Chapter 1 introduces the basic concepts of linear algebra, including matrices, vectors, and linear equations. Chapter 2 covers matrix operations, including matrix addition, multiplication, and inversion. Chapter 3 discusses the properties of matrices, such as determinant, eigenvalues, and eigenvectors. Chapter 4 introduces the concept of linear programming and its applications to engineering problems. Chapter 5 covers the theory of group representation and its applications to engineering problems.

Each chapter includes examples and exercises to help the reader understand the concepts and apply them to real-world problems. The examples are drawn from various engineering applications, such as computer science, electrical engineering, mechanical engineering, and civil engineering.

In conclusion, this book provides a comprehensive and up-to-date introduction to linear algebraic methods for engineering. It is an essential resource for students, researchers, and practitioners in the fields of engineering, mathematics, and science.

ISBN-13: 9789811257988