1st Edition

Advanced Linear Algebra for Engineers with MATLAB

By Sohail A. Dianat, Eli Saber Copyright 2009
    372 Pages 3 Color & 73 B/W Illustrations
    by CRC Press

    346 Pages 3 Color & 73 B/W Illustrations
    by CRC Press

    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.

    Matrices, Matrix Algebra, and Elementary Matrix Operations

    Basic Concepts and Notation

    Matrix Algebra

    Elementary Row Operations

    Solution of System of Linear Equations

    Matrix Partitions

    Block Multiplication

    Inner, Outer, and Kronecker Products

    Determinants, Matrix Inversion and Solutions to Systems of Linear Equations

    Determinant of a Matrix

    Matrix Inversion

    Solution of Simultaneous Linear Equations

    Applications: Circuit Analysis

    Homogeneous Coordinates System

    Rank, Null Space and Invertibility of Matrices

    Special Matrices with Applications

    Derivatives and Gradients

    Linear Vector Spaces

    Linear Vector Space

    Span of a Set of Vectors

    Normed Vector Spaces

    Inner Product Spaces


    Matrix Factorization

    Eigenvalues and Eigenvectors

    Matrices as Linear Transformations

    Eigenvalues and Eigenvectors

    Matrix Diagonalization

    Special Matrices

    Singular Value Decomposition (SVD)

    Numerical Computation of Eigenvalues and Eigenvectors

    Properties of Eigenvalues and Eigenvectors of Different

    Classes of Matrices


    Matrix Polynomials and Functions of Square Matrices

    Matrix Polynomials

    Cayley–Hamilton Theorem

    Functions of Matrices

    The State Space Modeling of Linear Continuous-time Systems

    State Space Representation of Discrete-time Systems

    Controllability of LTI Systems

    Observability of LTI Systems

    Introduction to Optimization

    Stationary Points of Functions of Several Variables

    Least-Square (LS) Technique

    Total Least-Squares (TLS)

    Eigen Filters

    Stationary Points with Equality Constraints

    Appendix A: The Laplace Transform

    Appendix B: The z-Transform




    Dianat, Sohail A.; Saber, Eli