Course Content

Lecture 1

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The Column Space of A Contains All Vectors Ax

Lecture 2

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Multiplying and Factoring Matrices

Lecture 3

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Orthonormal Columns in Q Give Q’Q = I

Lecture 4

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Eigenvalues and Eigenvectors

Lecture 5

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Positive Definite and Semidefinite Matrices

Lecture 6

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Singular Value Decomposition (SVD)

Lecture 7

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Eckart-Young: The Closest Rank k Matrix to A

Lecture 8

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Norms of Vectors and Matrices

Lecture 9

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Four Ways to Solve Least Squares Problems

Lecture 10

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Survey of Difficulties with Ax = b

Lecture 11

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Minimizing ‖x‖ Subject to Ax = b

Lecture 12

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Computing Eigenvalues and Singular Values

Lecture 13

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Randomized Matrix Multiplication

Lecture 14

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Low Rank Changes in A and Its Inverse

Lecture 15

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Matrices A(t) Depending on t, Derivative = dA/dt

Lecture 16

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Derivatives of Inverse and Singular Values

Lecture 17

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Rapidly Decreasing Singular Values

Lecture 18

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Counting Parameters in SVD, LU, QR, Saddle Points

Lecture 19

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Saddle Points Continued, Maxmin Principle

Lecture 20

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Definitions and Inequalities

Lecture 21

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Minimizing a Function Step by Step

Lecture 22

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Gradient Descent: Downhill to a Minimum

Lecture 23

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Accelerating Gradient Descent (Use Momentum)

Lecture 24

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Linear Programming and Two-Person Games

Lecture 25

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Stochastic Gradient Descent

Lecture 26

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Structure of Neural Nets for Deep Learning

Lecture 27

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Backpropagation: Find Partial Derivatives

Lecture 28

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Completing a Rank-One Matrix, Circulants!

Lecture 29

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Eigenvectors of Circulant Matrices: Fourier Matrix

Lecture 30

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ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule

Lecture 31

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Neural Nets and the Learning Function

Lecture 32

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Distance Matrices, Procrustes Problem

Lecture 33

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Finding Clusters in Graphs

Lecture 34

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Alan Edelman and Julia Language

Data Science 2021 : Complete Data Science & Machine Learning

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