| Sep 6 |
1.1, 1.2 |
Fields, vector spaces |
| Sep 10 |
1.2–1.3 |
Properties of vector spaces, linear combinations |
| Sep 13 |
1.4, 1.5 |
Linear combinations, subspaces |
| Sep 17 |
1.5, 2.1 |
Direct sums, linear maps |
| Sep 20 |
2.2, 2.3 |
Kernel and image, vector spaces of linear maps |
| Sep 24 |
2.4, 3.1 |
Isomorphisms, spans |
| Sep 27 |
3.2, 3.3 |
Linear dependence/independence, finitely generated vector spaces |
| Oct 1 |
3.4 |
Basis and dimension |
| Oct 4 |
3.4, 3.5 |
Basis and dimension, the Dimension Theorem |
| Oct 11 |
3.5–3.7 |
The Dimension Theorem, dimensions of spaces of linear maps, dual spaces |
| Oct 15 |
3.7, 4.1 |
Dual spaces, the matrix of a linear map |
| Oct 18 |
4.1, 4.2 |
The matrix of a linear map, similar matrices |
| Oct 22–26 |
Reading week |
| Oct 29 |
4.3, 4.4 |
Gaussian elimination, the rank of a matrix |
| Nov 1 |
5.1, 5.2 |
Multilinear maps, the determinant |
| Nov 5 |
1.1–4.4 |
Midterm test |
| Nov 8 |
5.3, 5.4 |
Properties of the determinant |
| Nov 12 |
6.1 |
Inner product spaces |
| Nov 15 |
6.2 |
Orthogonality |
| Nov 19 |
6.3 |
Adjoints |
| Nov 22 |
7.1 |
Eigenvectors, eigenvalues, and diagonalization |
| Nov 26 |
7.2 |
Criteria for diagonalization |
| Nov 29 |
7.3, 7.4 |
Self-adjoint operators and symmetric matrices |
| Dec 3 |
7.4, 7.5 |
Diagonalization of self-adjoint operators, rigid motions |
| Dec 5 |
N/A |
Review (Review questions, solutions) |