| 1 | The Geometry of Linear Equations | |
| 2 | Elimination with Matrices | |
| 3 | Matrix Operations and Inverses | |
| 4 | LU and LDU Factorization | Problem set 1 due |
| 5 | Transposes and Permutations | |
| 6 | Vector Spaces and Subspaces | |
| 7 | The Nullspace: Solving Ax = 0 | Problem set 2 due |
| 8 | Rectangular PA = LU and Ax = b | |
| 9 | Row Reduced Echelon Form | |
| 10 | Basis and Dimension | Problem set 3 due |
| 11 | The Four Fundamental Subspaces | |
| 12 | Exam 1: Chapters 1 to 3.5 | |
| 13 | Graphs and Networks | |
| 14 | Orthogonality | |
| 15 | Projections and Subspaces | |
| 16 | Least Squares Approximations | Problem set 4 due |
| 17 | Gram-Schmidt and A = QR | |
| 18 | Properties of Determinants | |
| 19 | Formulas for Determinants | Problem set 5 due |
| 20 | Applications of Determinants | |
| 21 | Eigenvalues and Eigenvectors | |
| 22 | Exam Review | Problem set 6 due |
| 23 | Exam 2: Chapters 1-5 | |
| 24 | Diagonalization | |
| 25 | Markov Matrices | |
| 26 | Fourier Series and Complex Matrices | |
| 27 | Differential Equations | |
| 28 | Symmetric Matrices | Problem set 7 due |
| 29 | Positive Definite Matrices | |
| 30 | Matrices in Engineering | Problem set 8 due |
| 31 | Singular Value Decomposition | |
| 32 | Similar Matrices | |
| 33 | Linear Transformations | Problem set 9 due |
| 34 | Choice of Basis | |
| 35 | Exam Review | |
| 36 | Exam 3: Chapters 1-8 (8.1, 2, 3, 5) | |
| 37 | Fast Fourier Transform | |
| 38 | Linear Programming | |
| 39 | Numerical Linear Algebra | |
| 40 | Final Exams | |