Introduction to Applied Linear Algebra. Vectors, Matrices, and Least Squares

Description

Cover Contents Preface I Vectors Vectors Vectors Vector addition Scalar-vector multiplication Inner product Complexity of vector computations Exercises Linear functions Linear functions Taylor approximation Regression model Exercises Norm and distance Norm Distance Standard deviation Angle Complexity Exercises Clustering Clustering A clustering objective The k-means algorithm Examples Applications Exercises Linear independence Linear dependence Basis Orthonormal vectors Gram–Schmidt algorithm Exercises II Matrices Matrices Matrices Zero and identity matrices Transpose, addition, and norm Matrix-vector multiplication Complexity Exercises Matrix examples Geometric transformations Selectors Incidence matrix Convolution Exercises Linear equations Linear and affine functions Linear function models Systems of linear equations Exercises Linear dynamical systems Linear dynamical systems Population dynamics Epidemic dynamics Motion of a mass Supply chain dynamics Exercises Matrix multiplication Matrix-matrix multiplication Composition of linear functions Matrix power QR factorization Exercises Matrix inverses Left and right inverses Inverse Solving linear equations Examples Pseudo-inverse Exercises III Least squares Least squares Least squares problem Solution Solving least squares problems Examples Exercises Least squares data fitting Least squares data fitting Validation Feature engineering Exercises Least squares classification Classification Least squares classifier Multi-class classifiers Exercises Multi-objective least squares Multi-objective least squares Control Estimation and inversion Regularized data fitting Complexity Exercises Constrained least squares Constrained least squares problem Solution Solving constrained least squares problems Exercises Constrained least squares applications Portfolio optimization Linear quadratic control Linear quadratic state estimation Exercises Nonlinear least squares Nonlinear equations and least squares Gauss–Newton algorithm Levenberg–Marquardt algorithm Nonlinear model fitting Nonlinear least squares classification Exercises Constrained nonlinear least squares Constrained nonlinear least squares Penalty algorithm Augmented Lagrangian algorithm Nonlinear control Exercises Appendices Notation Complexity Derivatives and optimization Derivatives Optimization Lagrange multipliers Further study Index