Chapter 1: Linear Algebra Highlights
1.1 Multiplication Ax using columns of matrix A
1.2 Matrix Multiplication AB
1.3 Four basic subspaces
1.4 Elimination and A=LU
1.5 Orthogonal matrices and subspaces
1.6 Eigenvalues ​​and Eigenvectors
1.7 Symmetric positive definite matrix
1.8 Singular Values ​​and Singular Vectors in Singular Value Decomposition
1.9 Principal components and optimal low-rank matrices
1.10 Rayleigh Quotients and Generalized Eigenvalues
1.11 Norms of Vectors, Functions, and Matrices
1.12 Decomposition of Matrices and Tensors: Quantity and Sparseness

Chapter 2: Calculating Large Matrices
2.1 Numerical linear algebra
2.2 Four Least Squares
2.3 Three bases of thermal space
2.4 Randomized linear algebra

Chapter 3: Low-Rank and Compressed Sensing
3.1 Changes in A^{-1} due to changes in A
3.2 Eigenvalue interlacing and low-rank signals
3.3 Rapidly decreasing singular values
3.4 Decomposition algorithm for l²+l¹
3.5 Compressed Sensing and Matrix Completion

Chapter 4 Special Matrices
4.1 Fourier Transform: Discrete and Continuous
4.2 Movement matrix and circulation matrix
4.3 Kronecker product AB
4.4 Sine and cosine transformations via Kronecker sums
4.5 Toeplitz matrices and shift-invariant filters
4.6 Graphs, the Laplacian, and Kirchhoff's Laws
4.7 Clustering using spectral methods and K-means
4.8 Rank 1 Matrix Completion
4.9 Orthogonal Procrustes Problem
4.10 Distance matrix


Chapter 5 Probability and Statistics
5.1 Mean, Variance, and Probability
5.2 Probability distribution
5.3 Moment generating function, cumulative generating function, and statistical inequalities
5.4 Covariance matrix and joint probability
5.5 Multivariate Normal Distribution and Weighted Least Squares
5.6 Markov chain

Chapter 6 Optimization
6.1 Minimum Problems: Convexity and Newton's Method
6.2 Lagrange multipliers and cost derivatives
6.3 Linear programming, game theory, and duality
6.4 Gradient descent to the minimum
6.5 Stochastic Gradient Descent and ADAM

Chapter 7: Learning from Data
7.1 Structure of deep neural networks
7.2 Convolutional Neural Networks
7.3 Backpropagation and the chain rule
7.4 Hyperparameters: Fateful Decisions
7.5 The World of Machine Learning


Appendix A References
Appendix B Eigenvalues ​​and Singular Values ​​of Rank 1 Matrices
Appendix C: Code and Algorithms for Numerical Linear Algebra
Appendix D Counting the Number of Parameters in Basic Decomposition
Appendix E: List of Books on Machine Learning

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Uncovering the relationship between linear algebra and deep learning!

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· College or graduate students in science and engineering fields interested in machine learning, deep learning, and data science
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Overseas book reviews
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“My only complaint about this book is, ‘Why did it only come out now?’”

- Volker H.
Schultz (Volker H.
Professor Schulz (University of Trier, Germany), excerpt from a book review by the Society for Industrial and Applied Mathematics (SIAM)


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