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