1st Edition
Advanced Linear Algebra for Engineers with MATLAB
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
Orthogonality
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
Applications
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
Bibliography
Index
Biography
Dianat, Sohail A.; Saber, Eli
