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14 Low Rank Changes in A and Its Inverse

Course Introduction of 18 065 by Professor Strang

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Lecture 1 The Column Space of A Contains All Vectors Ax

Lecture 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

Lecture 8 Norms of Vectors and Matrices

9 Four Ways to Solve Least Squares Problems

Lecture 10 Survey of Difficulties with Ax b

Lecture 11 Minimizing ‖x‖ Subject to Ax b

12 Computing Eigenvalues and Singular Values

Lecture 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

Lecture 17 Rapidly Decreasing Singular Values

Lecture 18 Counting Parameters in SVD LU QR Saddle Points

19 Saddle Points Continued Maxmin Principle

20 Definitions and Inequalities

Lecture 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

25 Stochastic Gradient Descent

26 Structure of Neural Nets for Deep Learning

27 Backpropagation Find Partial Derivatives

Lecture 30 Completing a Rank One Matrix Circulants

31 Eigenvectors of Circulant Matrices Fourier Matrix

Lecture 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

Lecture 36 Alan Edelman and Julia Language

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