Introduction to Applied Linear Algebra

Höfundar: Stephen Boyd; Lieven Vandenberghe (Útgáfa: 0)
Introduction to Applied Linear Algebra

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This groundbreaking textbook combines straightforward explanations with a wealth of practical examples to offer an innovative approach to teaching linear algebra. Requiring no prior knowledge of the subject, it covers the aspects of linear algebra - vectors, matrices, and least squares - that are needed for engineering applications, discussing examples across data science, machine learning and artificial intelligence, signal and image processing, tomography, navigation, control, and finance.

The numerous practical exercises throughout allow students to test their understanding and translate their knowledge into solving real-world problems, with lecture slides, additional computational exercises in Julia and MATLABĀ®, and data sets accompanying the book online. Suitable for both one-semester and one-quarter courses, as well as self-study, this self-contained text provides beginning students with the foundation they need to progress to more advanced study.

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Útgefandi
Cambridge University Press
ISBN
9781108693943
Print ISBN
9781316518960
Format
Page Fidelity (PDF)
Útgáfa
0
Höfundar
Stephen Boyd; Lieven Vandenberghe
Tungumál
English
Útgefið
2018-06-07
Prent takmörkun á líftíma
10

Kaflar

  • 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