Advanced Linear Algebra for Engineers with MATLAB

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