Matrix Methods in Data Analysis, Signal Processing, and Machine Learning

The Column Space of A Contains All Vectors Ax

Multiplying and Factoring Matrices 

Orthonormal Columns in Q Give Q′Q=I

Eigenvalues and Eigenvectors

Positive Definite and Semidefinite Matrices

Singular Value Decomposition (SVD)

Eckart-Young: The Closest Rank k Matrix to A

Norms of Vectors and Matrices

Four Ways to Solve Least Squares Problems

Survey of Difficulties with Ax=b

Minimizing ‖x‖ Subject to Ax=b

Computing Eigenvalues and Singular Values

Randomized Matrix Multiplication

Low Rank Changes in A and Its Inverse

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

Derivatives of Inverse and Singular Values

Rapidly Decreasing Singular Values

Counting Parameters in SVD, LU, QR, Saddle Points

Saddle Points Continued, Maxmin Principle

Definitions and Inequalities

Minimizing a Function Step by Step

Gradient Descent: Downhill to a Minimum

Accelerating Gradient Descent (Use Momentum)

Linear Programming and Two-Person Games

Stochastic Gradient Descent

Structure of Neural Nets for Deep Learning

Backpropagation: Find Partial Derivatives

Computing in Class [No video available]

Computing in Class (cont.) [No video available]

Completing a Rank-One Matrix, Circulants!

Eigenvectors of Circulant Matrices: Fourier Matrix

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

Neural Nets and the Learning Function

Distance Matrices, Procrustes Problem

Finding Clusters in Graphs

Alan Edelman and Julia Language