Linear Algebra and Learning from Data
Publisher: Wellesley - Cambridge Press
Published: 2019
Language: eng
Format: Hardcover
Number of pages: 432
ISBN-13: 9780692196380
Table of contents: title: Deep Learning and Neural Nets
pagenum: iii; title: Preface and Acknowledgments
pagenum: vi; label: Part I
title: Highlights of Linear Algebra
pagenum: 1; label: I.1
title: Multiplication \(Ax\) Using Columns of \(A\)
pagenum: 2; label: I.2
title: Matrix-Matrix Multiplication \(AB\)
pagenum: 9; label: I.3
title: The Four Fundamental Subspaces
pagenum: 14; label: I.4
title: Elimination and \(A = LU\)
pagenum: 21; label: I.5
title: Orthogonal Matrices and Subspaces
pagenum: 29; label: I.6
title: Eigenvalues and Eigenvectors
pagenum: 36; label: I.7
title: Symmetric Positive Definite Matrices
pagenum: 44; label: I.8
title: Singular Values and Singular Vectors in the SVD
pagenum: 56; label: I.9
title: Principal Components and the Best Low Rank Matrix
pagenum: 71; label: I.10
title: Rayleigh Quotients and Generalized Eigenvalues
pagenum: 81; label: I.11
title: Norms of Vectors and Functions and Matrices
pagenum: 88; label: I.12
title: Factoring Matrices and Tensors: Positive and Sparse
pagenum: 97; label: Part II
title: Computations with Large Matrices
pagenum: 113; label: II.1
title: Numerical Linear Algebra
pagenum: 115; label: II.2
title: Least Squares: Four Ways
pagenum: 124; label: II.3
title: Three Bases for the Column Space
pagenum: 138; label: II.4
title: Randomized Linear Algebra
pagenum: 146; label: Part III
title: Low Rank and Compressed Sensing
pagenum: 159; label: III.1
title: Changes in \(A^{-1}\) from Changes in \(A\)
pagenum: 160; label: III.2
title: Interlacing Eigenvalues and Low Rank Signals
pagenum: 168; label: III.3
title: Rapidly Decaying Singular Values
pagenum: 178; label: III.4
title: Split Algorithms for \(\ell^2 + \ell^1\)
pagenum: 184; label: III.5
title: Compressed Sensing and Matrix Completion
pagenum: 195; label: Part IV
title: Special Matrices
pagenum: 203; label: IV.1
title: Fourier Transforms: Discrete and Continuous
pagenum: 204; label: IV.2
title: Shift Matrices and Circulant Matrices
pagenum: 213; label: IV.3
title: The Kronecker Product \(A \otimes B\)
pagenum: 221; label: IV.4
title: Sine and Cosine Transforms from Kronecker Sums
pagenum: 228; label: IV.5
title: Toeplitz Matrices and Shift Invariant Filters
pagenum: 232; label: IV.6
title: Graphs and Laplacians and Kirchhoff's Laws
pagenum: 239; label: IV.7
title: Clustering by Spectral Methods and k-means
pagenum: 245; label: IV.8
title: Completing Rank One Matrices
pagenum: 255; label: IV.9
title: The Orthogonal Procrustes Problem
pagenum: 257; label: IV.10
title: Distance Matrices
pagenum: 259; label: Part V
title: Probability and Statistics
pagenum: 263; label: V.1
title: Mean, Variance, and Probability
pagenum: 264; label: V.2
title: Probability Distributions
pagenum: 275; label: V.3
title: Moments, Cumulants, and Inequalities of Statistics
pagenum: 284; label: V.4
title: Covariance Matrices and Joint Probabilities
pagenum: 294; label: V.5
title: Multivariate Gaussian and Weighted Least Squares
pagenum: 304; label: V.6
title: Markov Chains
pagenum: 311; label: Part VI
title: Optimization
pagenum: 321; label: VI.1
title: Minimum Problems: Convexity and Newton's Method
pagenum: 324; label: VI.2
title: Lagrange Multipliers: Derivatives of the Cost
pagenum: 333; label: VI.3
title: Linear Programming, Game Theory, and Duality
pagenum: 338; label: VI.4
title: Gradient Descent Toward the Minimum
pagenum: 344; label: VI.5
title: Stochastic Gradient Descent and ADAM
pagenum: 359; label: Part VII
title: Learning from Data
pagenum: 371; label: VII.1
title: The Construction of Deep Neural Networks
pagenum: 375; label: VII.2
title: Convolutional Neural Nets
pagenum: 387; label: VII.3
title: Backpropagation and the Chain Rule
pagenum: 397; label: VII.4
title: Hyperparameters: The Fateful Decisions
pagenum: 407; label: VII.5
title: The World of Machine Learning
pagenum: 413; title: Books on Machine Learning
pagenum: 416; title: Eigenvalues and Singular Values: Rank One
pagenum: 417; title: Codes and Algorithms for Numerical Linear Algebra
pagenum: 418; title: Counting Parameters in the Basic Factorizations
pagenum: 419; title: Index of Authors
pagenum: 420; title: Index
pagenum: 423; title: Index of Symbols
pagenum: 432