| 1 | The Column Space of \(A\) Contains All Vectors \(A\boldsymbol{x}\) |
| 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 \(A\boldsymbol{x} = \boldsymbol{b}\) |
| 11 | Minimizing \(‖\boldsymbol{x}‖\) Subject to \(A\boldsymbol{x} = \boldsymbol{b}\) |
| 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 |
| 25 | Stochastic Gradient Descent |
| 26 | Structure of Neural Nets for Deep Learning |
| 27 | Backpropagation: Find Partial Derivatives |
| 28 | Computing in Class [No video available] |
| 29 | Computing in Class (cont.) [No video available] |
| 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 |
