Matrix Methods in Data Analysis, Signal Processing, and Machine Learning
A) Course Introduction of 18.065 by Professor Strang B) An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,... 01. The Column Space of A Contains All Vectors Ax 02. Multiplying and Factoring Matrices 03. Orthonormal Columns in Q Give Q'Q 04. Eigenvalues and Eigenvectors 05. Positive Definite and Semidefinite Matrices 06. Singular Value Decomposition (SVD) 07. The Closest Rank k Matrix to A 08. Norms of Vectors and Matrices 09. Four Ways to Solve Least Squares Problems 10. Survey of Difficulties with Ax 11. Minimizing _x_ Subject to Ax 12. Computing Eigenvalues and Singular Values 13. Randomized Matrix Multiplication 14. Low Rank Changes in A and Its Inverse 15. Matrices A(t) Depending on t, Derivative 16. Derivatives of Inverse and Singular Values 17. Rapidly Decreasing Singular Values 18. Counting Parameters in SVD, LU, QR, Saddle Points 19. Saddle Points Continued, Maxmin Principle 20. Definitions and Inequalities 21. Minimizing a Function Step by Step 22. Downhill to a Minimum 23. Accelerating Gradient Descent (Use Momentum) 24. Linear Programming and Two-Person Games 25. Stochastic Gradient Descent 26. Structure of Neural Nets for Deep Learning 27. Find Partial Derivatives 30. Completing a Rank-One Matrix, Circulants! 31. Fourier Matrix 32. ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule 33. Neural Nets and the Learning Function 34. Distance Matrices, Procrustes Problem 35. Finding Clusters in Graphs 36. Alan Edelman and Julia Language