Advanced Linear Algebra for Engineers with MATLAB

Sohail A. Dianat, Eli Saber, Sohail Dianat

• Publisher: CRC Press
• Year: 2017
• Print ISBN: 9781420095234
• eBook ISBN: 9781351834377
• Topic: Mathematics
• Subtopic: Electrical Engineering & Telecommunications
• Index: Mathematics

Arming readers with both theoretical and practical knowledge, Advanced Linear Algebra for Engineers with MATLAB® provides real-life problems that readers can use to model and solve engineering and scientific problems in fields ranging from signal processing and communications to electromagnetics and social and health sciences.

Facilitating a unique understanding of rapidly evolving linear algebra and matrix methods, this book:

• Outlines the basic concepts and definitions behind matrices, matrix algebra, elementary matrix operations, and matrix partitions, describing their potential use in signal and image processing applications
• Introduces concepts of determinants, inverses, and their use in solving linear equations that result from electrical and mechanical-type systems
• Presents special matrices, linear vector spaces, and fundamental principles of orthogonality, using an appropriate blend of abstract and concrete examples and then discussing associated applications to enhance readers' visualization of presented concepts
• Discusses linear operators, eigenvalues, and eigenvectors, and explores their use in matrix diagonalization and singular value decomposition
• Extends presented concepts to define matrix polynomials and compute functions using several well-known methods, such as Sylvester's expansion and Cayley-Hamilton
• Introduces state space analysis and modeling techniques for discrete and continuous linear systems, and explores applications in control and electromechanical systems, to provide a complete solution for the state space equation
• Shows readers how to solve engineering problems using least square, weighted least square, and total least square techniques
• Offers a rich selection of exercises and MATLAB® assignments that build a platform to enhance readers' understanding of the material

Striking the appropriate balance between theory and real-life applications, this book provides both advanced students and professionals in the field with a valuable reference that they will continually consult.

Table of contents

• Cover Page
• Half title
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• Authors
• 1 Matrices, Matrix Algebra, and Elementary Matrix Operations
• 2 Determinants, Matrix Inversion and Solutions to Systems of Linear Equations
• 3 Linear Vector Spaces
• 4 Eigenvalues and Eigenvectors
• 5 Matrix Polynomials and Functions of Square Matrices
• 6 Introduction to Optimization
• Appendix A: The Laplace Transform
• Appendix B: The z-Transform
• Bibliography
• Index
• Color Figure