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MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018

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Last updated on Aug 19, 2019
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Course Introduction of 18.065 by Professor Strang
7:04
An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,...
8:07
Lecture 1: The Column Space of A Contains All Vectors Ax
52:15
Lecture 2: Multiplying and Factoring Matrices
48:26
3. Orthonormal Columns in Q Give Q'Q = I
49:24
4. Eigenvalues and Eigenvectors
48:56
5. Positive Definite and Semidefinite Matrices
45:28
6. Singular Value Decomposition (SVD)
53:34
7. Eckart-Young: The Closest Rank k Matrix to A
47:16
Lecture 8: Norms of Vectors and Matrices
49:21
9. Four Ways to Solve Least Squares Problems
49:51
Lecture 10: Survey of Difficulties with Ax = b
49:36
Lecture 11: Minimizing ‖x‖ Subject to Ax = b
50:22
12. Computing Eigenvalues and Singular Values
49:28
Lecture 13: Randomized Matrix Multiplication
52:24
14. Low Rank Changes in A and Its Inverse
50:34
15. Matrices A(t) Depending on t, Derivative = dA/dt
50:52
16. Derivatives of Inverse and Singular Values
43:08
Lecture 17: Rapidly Decreasing Singular Values
50:34
Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points
49:00
19. Saddle Points Continued, Maxmin Principle
52:13
20. Definitions and Inequalities
55:01
Lecture 21: Minimizing a Function Step by Step
53:45
22. Gradient Descent: Downhill to a Minimum
52:44
23. Accelerating Gradient Descent (Use Momentum)
49:02
24. Linear Programming and Two-Person Games
53:34
25. Stochastic Gradient Descent
53:03
26. Structure of Neural Nets for Deep Learning
53:17
27. Backpropagation: Find Partial Derivatives
52:38
Lecture 30: Completing a Rank-One Matrix, Circulants!
49:53
31. Eigenvectors of Circulant Matrices: Fourier Matrix
52:37
Lecture 32: ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule
47:19
33. Neural Nets and the Learning Function
56:07
34. Distance Matrices, Procrustes Problem
29:17
35. Finding Clusters in Graphs
34:49
Lecture 36: Alan Edelman and Julia Language
38:11