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Matrix Methods for Data Analysis & ML

MIT 18.065, Gilbert Strang · Math · Fall 2029 · Planned

Lectures

  1. Course Introduction to Matrix Methods for Data Analysis (7:04)
  2. Interview: Gilbert Strang on Teaching Matrix Methods (8:06)
  3. Lecture 1: The Column Space of A Contains All Vectors Ax (52:14)
  4. Lecture 2: Multiplying and Factoring Matrices (48:25)
  5. Lecture 3: Orthonormal Columns Give Q'Q = I (49:24)
  6. Lecture 4: Eigenvalues and Eigenvectors (48:55)
  7. Lecture 5: Positive Definite and Semidefinite Matrices (45:27)
  8. Lecture 6: Singular Value Decomposition (SVD) (53:33)
  9. Lecture 7: Eckart-Young, the Closest Rank k Matrix to A (47:16)
  10. Lecture 8: Norms of Vectors and Matrices (49:21)
  11. Lecture 9: Four Ways to Solve Least Squares Problems (49:51)
  12. Lecture 10: Survey of Difficulties with Ax = b (49:36)
  13. Lecture 11: Minimizing ‖x‖ Subject to Ax = b (50:22)
  14. Lecture 12: Computing Eigenvalues and Singular Values (49:27)
  15. Lecture 13: Randomized Matrix Multiplication (52:24)
  16. 14. Low Rank Changes in A and Its Inverse (50:34)
  17. Lecture 17: How Eigenvalues Change When a Matrix Changes (50:51)
  18. Lecture 16: Derivatives of Inverse and Singular Values (43:08)
  19. Lecture 17: Rapidly Decreasing Singular Values (50:33)
  20. Lecture 18: Counting Parameters in SVD, LU, QR, Saddle Points (49:00)
  21. Lecture 19: Saddle Points Continued, Maxmin Principle (52:13)
  22. Lecture 20: Definitions and Inequalities (55:01)
  23. Lecture 21: Minimizing a Function Step by Step (53:44)
  24. Lecture 22: Gradient Descent - Downhill to a Minimum (52:43)
  25. Lecture 23: Accelerating Gradient Descent (Use Momentum) (49:01)
  26. Lecture 24: Linear Programming and Two-Person Games (53:33)
  27. Lecture 25: Stochastic Gradient Descent (53:02)
  28. Lecture 26: Structure of Neural Nets for Deep Learning (53:17)
  29. Lecture 27: Backpropagation, Finding Partial Derivatives (52:38)
  30. Lecture 30: Completing a Rank-One Matrix, Circulants (49:52)
  31. Lecture 31: Eigenvectors of Circulant Matrices, the Fourier Matrix (52:36)
  32. Lecture 32: ImageNet's CNN and the Convolution Rule (47:18)
  33. Lecture 33: Neural Nets and the Learning Function (56:07)
  34. Lecture 34: Distance Matrices, the Procrustes Problem (29:17)
  35. Lecture 35: Finding Clusters in Graphs (34:49)
  36. Lecture 36: Alan Edelman and Julia Language (38:11)

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