| 1 | Systems of Linear Equations | |
| 2 | Echelon Form | |
| 3 | Matrices | |
| 4 | Matrices (cont.) | |
| 5 | Solution Spaces | Problem set 1 due |
| 6 | Inverses and Transposes | |
| 7 | Fields and Spans | |
| 8 | Vector Spaces | Problem set 2 due |
| 9 | Linear Independence | |
| 10 | Basis and Dimension | |
| 11 | Coordinates | Problem set 3 due |
| 12 | Review for Quiz 1 | |
| 13 | Quiz 1 (Chapters 0-1) | |
| 14 | Determinants | |
| 15 | Permutations | |
| 16 | Determinants (cont.) | Problem set 4 due |
| 17 | Laplace Expansion | |
| 18 | Review for Quiz 2 | Problem set 5 due |
| 19 | Quiz 2 (Chapter 2) | |
| 20 | Linear Transformations | |
| 21 | Rank, Kernel, Image | |
| 22 | Matrix Representations | |
| 23 | Eigenspaces | |
| 24 | Eigenspaces (cont.) | Problem set 6 due |
| 25 | Diagonalization | |
| 26 | Cayley-Hamilton Theorem | |
| 27 | Jordan Canonical Form | |
| 28 | Review for Quiz 3 | Problem set 7 due |
| 29 | Quiz 3 (Chapter 3) | |
| 30 | Computing Generalized Eigenvectors | |
| 31 | Norms and Inner Products | |
| 32 | Norms and Inner Products (cont.) | |
| 33 | Orthogonal Bases | |
| 34 | Orthogonal Projections | |
| 35 | Isometries, Spectral Theory | |
| 36 | Singular Value Decomposition | Problem set 8 due |
| 37 | Polar Decomposition | |
| 38 | Review for the Final | |