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# Matrix Methods in Data Analysis, Signal Processing, and Machine Learning (Spring 2018)

## Course Features

• Video lectures
• Captions/transcript
• Assignments: problem sets (no solutions)

## Educator Features

• Instructor insights
• Podcast - audio

## Course Description

Linear algebra concepts are key for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization–and above all a full explanation of deep learning.

## Syllabus

Course Introduction of 18.065 by Professor Strang.
An Interview with Gilbert Strang on Teaching Matrix Methods in Data Analysis, Signal Processing,....
1. The Column Space of A Contains All Vectors Ax.
2. Multiplying and Factoring Matrices.
3. Orthonormal Columns in Q Give Q'Q = I.
4. Eigenvalues and Eigenvectors.
5. Positive Definite and Semidefinite Matrices.
6. Singular Value Decomposition (SVD).
7. Eckart-Young: The Closest Rank k Matrix to A.
8. Norms of Vectors and Matrices.
9. Four Ways to Solve Least Squares Problems.
10. Survey of Difficulties with Ax = b.
11. Minimizing _x_ Subject to Ax = b.
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 = dA/dt.
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. Gradient Descent: Downhill to a Minimum.
23. Accelerating Gradient Descent (Use Momentum).
24. Linear Programming and Two-Person Games.
26. Structure of Neural Nets for Deep Learning.
27. Backpropagation: Find Partial Derivatives.
30. Completing a Rank-One Matrix, Circulants!.
31. Eigenvectors of Circulant Matrices: 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.

### Taught by

Prof. Gilbert Strang

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