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

✍ Scribed by Stephen Boyd, Lieven Vandenberghe

• Publisher: Cambridge University Press
• Year: 2018
• Tongue: English
• Leaves: 474
• Category: Library

✦ Table of Contents

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