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• Half-title
• Title page
• Copyright information
• Dedication
• Contents
• Preface
• Part I Vectors
• Chapter 1 Vectors
• 1.1 Vectors
• 1.2 Vector addition
• 1.3 Scalar-vector multiplication
• 1.4 Inner product
• 1.5 Complexity of vector computations
• Exercises
• Chapter 2 Linear functions
• 2.1 Linear functions
• 2.2 Taylor approximation
• 2.3 Regression model
• Exercises
• Chapter 3 Norm and distance
• 3.1 Norm
• 3.2 Distance
• 3.3 Standard deviation
• 3.4 Angle
• 3.5 Complexity
• Exercises
• Chapter 4 Clustering
• 4.1 Clustering
• 4.2 A clustering objective
• 4.3 The k-means algorithm
• 4.4 Examples
• 4.5 Applications
• Exercises
• Chapter 5 Linear independence
• 5.1 Linear dependence
• 5.2 Basis
• 5.3 Orthonormal vectors
• 5.4 Gram–Schmidt algorithm
• Exercises
• Part II Matrices
• Chapter 6 Matrices
• 6.1 Matrices
• 6.2 Zero and identity matrices
• 6.3 Transpose, addition, and norm
• 6.4 Matrix-vector multiplication
• 6.5 Complexity
• Exercises
• Chapter 7 Matrix examples
• 7.1 Geometric transformations
• 7.2 Selectors
• 7.3 Incidence matrix
• 7.4 Convolution
• Exercises
• Chapter 8 Linear equations
• 8.1 Linear and affine functions
• 8.2 Linear function models
• 8.3 Systems of linear equations
• Exercises
• Chapter 9 Linear dynamical systems
• 9.1 Linear dynamical systems
• 9.2 Population dynamics
• 9.3 Epidemic dynamics
• 9.4 Motion of a mass
• 9.5 Supply chain dynamics
• Exercises
• Chapter 10 Matrix multiplication
• 10.1 Matrix-matrix multiplication
• 10.2 Composition of linear functions
• 10.3 Matrix power
• 10.4 QR factorization
• Exercises
• Chapter 11 Matrix inverses
• 11.1 Left and right inverses
• 11.2 Inverse
• 11.3 Solving linear equations
• 11.4 Examples
• 11.5 Pseudo-inverse
• Exercises
• Part III Least squares
• Chapter 12 Least squares
• 12.1 Least squares problem
• 12.2 Solution
• 12.3 Solving least squares problems
• 12.4 Examples
• Exercises
• Chapter 13 Least squares data fitting
• 13.1 Least squares data fitting
• 13.2 Validation
• 13.3 Feature engineering
• Exercises
• Chapter 14 Least squares classification
• 14.1 Classification
• 14.2 Least squares classifier
• 14.3 Multi-class classifiers
• Exercises
• Chapter 15 Multi-objective least squares
• 15.1 Multi-objective least squares
• 15.2 Control
• 15.3 Estimation and inversion
• 15.4 Regularized data fitting
• 15.5 Complexity
• Exercises
• Chapter 16 Constrained least squares
• 16.1 Constrained least squares problem
• 16.2 Solution
• 16.3 Solving constrained least squares problems
• Exercises
• Chapter 17 Constrained least squares applications
• 17.1 Portfolio optimization
• 17.2 Linear quadratic control
• 17.3 Linear quadratic state estimation
• Exercises
• Chapter 18 Nonlinear least squares
• 18.1 Nonlinear equations and least squares
• 18.2 Gauss–Newton algorithm
• 18.3 Levenberg–Marquardt algorithm
• 18.4 Nonlinear model fitting
• 18.5 Nonlinear least squares classification
• Exercises
• Chapter 19 Constrained nonlinear least squares
• 19.1 Constrained nonlinear least squares
• 19.2 Penalty algorithm
• 19.3 Augmented Lagrangian algorithm
• 19.4 Nonlinear control
• Exercises
• Appendices
• Appendix A Notation
• Appendix B Complexity
• Appendix C Derivatives and optimization
• C.1 Derivatives
• C.2 Optimization
• C.3 Lagrange multipliers
• Appendix D Further study
• Index