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