Matrices, Matrix Algebra, and Elementary Matrix Operations; Basic Concepts an 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.