1st Edition
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
Biography
Dianat, Sohail A.; Saber, Eli






