Applied Linear Algebra
MTH 415-001
Schedule and Topics Covered
| Date | Topic/Section | Assignments and Reading |
| 8/25 | Welcome, and Neurons | Read the Syllabus |
| 8/27 | Motivation: FNNs | DUE 8/29: Read Chapter 1 of Notes_v1 HW1 -- DUE 9/5: Do the 10 Exercises 1.2.2, 1.2.3, 2.1.2, 2.1.3, 2.1.4, 2.1.7, 2.1.8, 2.1.9, 2.2.1, 2.2.2 from Notes_v1 |
| 8/29 | The Complex Numbers | DUE 9/5: Read Sections 2.1 and 2.2 of Notes_v1 |
| 9/1 | Holiday - no class | |
| 9/3 | Inner Products and Cauchy-Schwarz | DUE 9/8: Read Section 2.3 of Notes_v1 |
| 9/5 | Norms, Spans, and Subspaces HW 1 DUE IN CLASS | HW2 -- DUE 9/12: Do the 14 Exercises 2.2.3, 2.2.4, 2.2.5, 2.2.6, 2.2.8, 2.2.9, 2.2.10, 2.2.11, 2.2.12, 2.2.13, 2.2.14, 2.3.1, 2.3.2, and 2.3.3 from Notes_v2 |
| 9/8 | Bases, Dimension, and Rank | DUE 9/12: Read Section 2.4 of Notes_v2 |
| 9/10 | Orthonormal Bases and the Pythagorean Theorem | |
| 9/12 | The Gram-Schmidt algorithm HW 2 DUE IN CLASS | HW3 -- DUE 9/19: Do the 10 Exercises 2.3.8, 2.3.9, 2.3.10, 2.3.11, 2.3.12, 2.3.13, 2.4.1, 2.4.3, 2.4.5, 2.4.6 from Notes_v3 |
| 9/15 | The QR Decomposition | DUE 9/19: Read Section 2.5 of Notes_v3 |
| 9/17 | Elementary Matrices and Gaussian Elimination | |
| 9/19 | Perpendicular Subspaces HW 3 DUE IN CLASS | HW4 -- DUE 9/26: Do the 10 Exercises 2.5.1, 2.5.2, 2.5.3, 2.5.4, 2.5.5, 2.5.6, 2.5.7, 2.6.1, 2.6.2, 2.6.3 from Notes_v4 |
| 9/22 | Orthogonal Projections | DUE 9/26: Read Section 2.6 of Notes_v4 |
| 9/24 | Least Squares Solutions | |
| 9/26 | The Four Fundamental Subspaces HW 4 DUE IN CLASS | HW5 -- DUE 10/3: Do the 10 Exercises 2.6.4, 2.6.5, 2.6.6, 2.6.7, 2.6.8, 2.6.9, 2.6.10, 2.6.11, 2.6.12, 2.7.1 from Notes_v5 |
| 9/29 | Spectral Theorem for Hermitian Matrices | DUE 10/1: Read Sections 2.7 and 2.8 of Notes_v5 |
| 10/1 | PSD Matrices | DUE 10/3: Read Sections 2.9 and 2.10 of Notes_v5 |
| 10/3 | Trace and Determinant HW 5 DUE IN CLASS | HW6 -- DUE 10/10: Do the 11 Exercises 2.7.2, 2.7.3, 2.7.4, 2.8.1, 2.8.3, 2.8.6, 2.9.1, 2.9.2, 2.9.3, 2.9.4, and 2.9.8 from Notes_v5. NOTE: For 2.9.8 assume A is also full rank. |
| 10/6 | Toward the SVD | DUE 10/10: Read pages 71 -- 76 of Notes_v5 |
| 10/8 | Properties of the SVD | DUE 10/13: Read Sections 3.1.1, 3.1.2, and 3.1.3 of Notes_v5 |
| 10/10 | Moore-Penrose Inverses HW 6 DUE IN CLASS | HW7 -- DUE 10/15: Do the 8 Exercises 2.10.1, 2.10.3, 2.10.5, 3.1.1, 3.1.2, 3.1.3, 3.1.4, 3.1.5 from Notes_v5 |
| 10/13 | Singular Values and Matrix Norms | STUDY |
| 10/15 | Midterm Review HW 7 DUE IN CLASS | STUDY |
| 10/17 | MIDTERM EXAM | PARTY |
| 10/20 | Fall Break - no class | |
| 10/22 | Optimal Low-Rank Approximation | DUE 10/24: Read Sections 3.4 and 3.5 of Notes_v6 |
| 10/24 | Condition Numbers and SVD Regularization | HW8 -- DUE 10/31: Do the 10 Exercises 3.1.7, 3.1.9, 3.1.10, 3.2.1, 3.2.2, 3.2.3, 3.2.4, 3.3.3, 3.3.4, 3.3.5 from Notes_v6 |
| 10/27 | Code Demo Log into Matlab | We will discuss these Matlab Files. |
| 10/29 | Linear Least-Squares Regression | DUE 10/31: Read Sections 3.6 and 3.7 of Notes_v7 |
| 10/31 | Linear Regression Cont'd HW 8 DUE IN CLASS | HW9 -- DUE 11/7: Do the 11 Exercises 3.4.1, 3.5.1, 3.5.2, 3.5.3, 3.5.4, 3.5.5, 3.5.6, 3.5.7, 3.5.8, 3.5.9, 3.5.10 from Notes_v7 |
| 11/3 | Jupyter Demo How do I run a Jupyter Notebook? | We will discuss LeastSquaresRegression.ipynb. |
| 11/5 | Toeplitz Matrices | DUE 11/10: Read Section 3.8 of Notes_v7 |
| 11/7 | DFT and Circulant Matrices HW 9 DUE IN CLASS | HW10 -- DUE 11/14: Do the 11 Exercises 3.6.1, 3.6.2, 3.6.3, 3.6.4, 3.6.5, 3.6.6, 3.6.7, 3.6.8, 3.7.1, 3.7.2, 3.7.3 from Notes_v7 |
| 11/10 | The FFT Algorithm | We will discuss some FFT C code. |
| 11/12 | Fast Multiplication of Toeplitz Matrices | DUE 11/17: Read Section 3.9 of Notes_v8 |
| 11/14 | Convex Functions HW 10 DUE IN CLASS | HW11 -- DUE 11/21: Do the 12 Exercises 3.7.4, 3.7.5, 3.7.6, 3.7.9, 3.7.10, 3.7.11, 3.7.12, 3.7.15, 3.7.16, 3.7.17, 3.7.20, and 3.7.21 from Notes_v8 |
| 11/17 | The Holder inequality | |
| 11/19 | Discrete Riesz-Thorin | DUE 11/24: Read Section 3.10 of Notes_v8 |
| 11/21 | Convolution Inequalities HW 11 DUE IN CLASS | HW12 -- DUE 12/5: Do the 14 Exercises 3.9.1, 3.9.2, 3.9.3, 3.9.4, 3.9.5, 3.9.6, 3.9.7, 3.9.9, 3.9.11, 3.10.1, 3.10.3, 3.10.4, 3.10.5, and 3.11.1 from Notes_v9 |
| 11/24 | Finite Metric Spaces | DUE 12/1: Read Section 3.11 of Notes_v9 |
| 11/26 | Isometric Embeddings | |
| 11/28 | Holiday - no class | |
| 12/1 | Fast Diameter Example | |
| 12/3 | Trading Accuracy for Space | |
| 12/5 | Final Review HW 12 DUE IN CLASS | |
| 12/10 | FINAL EXAM | 5:45 pm -- 7:45 pm in WH A318 |