Advanced Linear Algebra for Engineers with MATLAB

Content: 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