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
MIT A 2020 Vision of Linear Algebra, Spring 2020
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A) Course Introduction of 18.065 by Professor Strang