All problem sets in one file (PDF)
| LEC # | TOPICS | READINGS | ASSIGNMENTS |
|---|---|---|---|
| 1 | The Column Space of \(A\) Contains All Vectors \(A\boldsymbol{x}\) | Section I.1 | Problem Set I.1 (PDF) |
| 2 | Multiplying and Factoring Matrices | Section I.2 | Problem Set I.2 (PDF) |
| 3 | Orthonormal Columns in \(Q\) Give \(Q’Q= I\) | Section I.5 | Problem Set I.5 (PDF) |
| 4 | Eigenvalues and Eigenvectors | Section I.6 | Problem Set I.6 (PDF) |
| 5 | Positive Definite and Semidefinite Matrices | Section I.7 | Problem Set I.7 (PDF) |
| 6 | Singular Value Decomposition (SVD) | Section I.8 | Problem Set I.8 (PDF) |
| 7 | Eckart-Young: The Closest Rank \(k\) Matrix to \(A\) | Section I.9 | Problem Set I.9 (PDF) |
| 8 | Norms of Vectors and Matrices | Section I.11 | Problem Set I.11 (PDF) |
| 9 | Four Ways to Solve Least Squares Problems | Section II.2 | Problem Set II.2 Problems 2, 8, 9 (PDF) |
| 10 | Survey of Difficulties with \(A\boldsymbol{x} = \boldsymbol{b}\) | Introduction Chapter 2 | Problem Set II.2 Problems 12, 17 (PDF) |
| 11 | Minimizing \(‖\boldsymbol{x}‖\) Subject to \(A\boldsymbol{x} = \boldsymbol{b}\) | Section I.11 | Problem Set I.11 Problem 6 Problem Set II.2 Problem 10 (PDF) |
| 12 | Computing Eigenvalues and Singular Values | Section II.1 | Problem Set II.1 (PDF) |
| 13 | Randomized Matrix Multiplication | Section II.4 | Problem Set II.4 (PDF) |
| 14 | Low Rank Changes in \(A\) and Its Inverse | Section III.1 | Problem Set III.1 (PDF) |
| 15 | Matrices \(A(t)\) Depending on \(t\), Derivative = \(dA/dt\) | Sections III.1–III.2 | Problem Set III.2 Problems 1, 2, 5 (PDF) |
| 16 | Derivatives of Inverse and Singular Values | Sections III.1–III.2 | Problem Set III.2 Problems 3, 12 (PDF) |
| 17 | Rapidly Decreasing Singular Values | Section III.3 | Problem Set III.3 (PDF) |
| 18 | Counting Parameters in SVD, LU, QR, Saddle Points | Appendix, Section III.2 | Problem Set III.2 (PDF) |
| 19 | Saddle Points Continued, Maxmin Principle | Sections III.2, V.1 | Problem Set V.1 Problems 3, 8 (PDF) |
| 20 | Definitions and Inequalities | Sections V.1, V.3 | Problem Set V.1 Problems 10. 12 Problem Set V.3 Problem 3 (PDF) |
| 21 | Minimizing a Function Step by Step | Sections VI.1, VI.4 | Problem Set VI.1 (PDF) |
| 22 | Gradient Descent: Downhill to a Minimum | Section VI.4 | Problem Set VI.4 Problems 1, 6 (PDF) |
| 23 | Accelerating Gradient Descent (Use Momentum) | Section VI.4 | Problem Set VI.4 Problem 5 (PDF) |
| 24 | Linear Programming and Two-Person Games | Sections VI.2–VI.3 | Problem Set VI.2 Problem 1 |
| 25 | Stochastic Gradient Descent | Section VI.5 | Problem Set VI.5 (PDF) |
| 26 | Structure of Neural Nets for Deep Learning | Section VII.1 | Problem Set VII.1 (PDF) |
| 27 | Backpropagation to Find Derivative of the Learning Function | Section VII.2 | Problem Set VII.2 (PDF) |
| 28 | Computing in Class [No video available] | Section VII.2 and Appendix 3 | [No Problems Assigned] |
| 29 | Computing in Class (cont.) [No video available] | [No Readings] | [No Problems Assigned] |
| 30 | Completing a Rank-One Matrix, Circulants! | Sections IV.8, IV.2 | |
| 31 | Eigenvectors of Circulant Matrices: Fourier Matrix | Section IV.2 | Problem Set IV.2 Problems 3, 5 (PDF) |
| 32 | ImageNet is a Convolutional Neural Network (CNN), The Convolution Rule | Section IV.2 | Problem Set IV.2 Problem 4 (PDF) |
| 33 | Neural Nets and the Learning Function | Sections VII.1, IV.10 | |
| 34 | Distance Matrices, Procrustes Problem | Sections IV.9–IV.10 | Problem Set IV.9 (PDF) |
| 35 | Finding Clusters in Graphs | Sections IV.6–IV.7 | Problem Set IV.6 (PDF) |
| 36 | Alan Edelman and Julia Language | Sections III.3, VII.2 | [No Problems Assigned] |