| Date | Topic | Book | Homework | Practice Problems | |
|---|---|---|---|---|---|
| Jan. | 10 | Introduction to determinants | |||
| 12 | Axiomatic characterization of the determinant | ||||
| 13 | Bilinearity and determinants in ℝ2 | ||||
| 17 | Trilinearity and determinants in ℝ3 | §4.2 | |||
| 19 | The determinant in any dimension | §4.2 | |||
| 20 | Permutations and the determinant formula | §4.2 | H13 | ||
| 24 | Calculating the determinant | §4.2 | A13 | 1 – 15 | |
| 26 | More determinant calculations | §4.2 | 16 – 20, 22, 23, 26 – 29 | ||
| 27 | Cramer's Rule | §4.2 | H14 | 35 – 38, 57 – 60 | |
| 31 | The classical adjoint | §4.2 | A14 | 61 — 64 | |
| Feb. | 2 | Bases and coordinates | §6.3 | 1, 2, 3, 4 (part a only) | |
| 3 | Change of basis | §6.3 | H15 | 1, 2, 3, 4 (parts b, c, d, e) | |
| Feb. | 7 | Change of basis II | A15 | ||
| 9 | In-class exam #3 | ||||
| 10 | Iterating linear transformations | §3.7 | H16 | 5 – 8, 10 | |
| 14 | Eigenvalues and Eigenvectors | §4.3 | A16 | §4.1: 13–17 | |
| 16 | Finding Eigenvalues and Eigenvectors | §4.3 | 1–6 (parts a and b) | ||
| 17 | Diagonalization | §4.4 | H17 | 5–7 | |
| 21 | |||||
| 23 | Reading Week | ||||
| 24 | |||||
| 28 | Eigenspaces | §4.3 | A17 | 1–6 (parts c and d) | |
| Mar. | 2 | More Diagonalization | §4.4 | 8–15, 16–18 | |
| 3 | End of the proof on Diagonalization | §4.4 | H18 | ||
| 7 | Complex Numbers | App. C | A18 | ||
| 9 | Complex Eigenvalues and Eigenvectors | ||||
| 10 | Dominant Eigenvalues | §4.5 | H19 | 9–12 | |
| 14 | The Gerschgorin disk theorem | §4.5 | A19 | 47–50 | |
| 16 | In-class exam #4 | ||||
| 17 | Some Eigenapplications | §4.6 | H20 | 7–9 | |
| 21 | Introduction to abstract vector spaces | §6.1 | A20 | 5–10 | |
| 23 | Subspaces, bases, coordinates | §6.1-2 | §6.1: 29, 33, 35, 36 | ||
| 24 | Linear transformations | §6.4 | H21 | 5, 7, 8, 16 | |
| 28 | Dimension, Rank-nullity theorem | §6.5 | A21 | 3, 4, 10, 12 | |
| 30 | Inner product spaces | §7.1 | 1, 2, 5, 9, 10, 11 | ||
| 31 | Orthonormal bases | §5.1 | H22 | 1–6, 11–15 | |
| Apr. | 4 | Gram-Schmidt orthogonalization | §5.3 | A22 | 1–6, 11, 12 |
| 6 | Least-squares solutions | §7.3 | 19, 20, 23, 24 | ||
| 7 | Least-squares solutions II | §7.3 | H23 | ||
| 11 | A23 | ||||
| 13 | H24 | ||||
| 14 | A24 |