| Lec. | Date | Topics | Sec./pages |
|---|---|---|---|
| 1 | 1/9 | Vector spaces, subspaces, span - review. | 4.2 p.233-242 |
| 2 | 1/11 | Linear dependence and independence, basis and dimension - review. |
4.2 p.245-247, 4.3 p.253-256, 259-262 |
| - | 1/16 | -- MLK Day -- | |
| 3 | 1/18 | One-to-one, onto, and invertible functions. Linear transformations - review. |
5.1 p.285-289, 296-297 |
| 4 | 1/23 | Isomorphisms of vector spaces. Dot product. |
|
| 5 | 1/25 | Orthogonality, projections -- review. Orthogonal and orthonormal sets and bases. Gram-Schmidt algorithm. |
6.2 p.353-359 |
| 6 | 1/30 | Fourier series - vector space approach. | |
| 7 | 2/1 | Orthogonal matrices. Orthogonal complements. |
6.2 p.362-364 6.3 p.378-381 |
| 8 | 2/6 | Sums and intersections of subspaces. | 6.3 |
| 9 | 2/8 | Sums and intersections of subspaces. Direct sums. |
6.3 |
| 10 | 2/13 | Review | |
| 11 | 2/15 | Exam 1 | |
| 12 | 2/20 | Exam 1 - discussion. The matrix of a linear transformation relative to the standard bases - review. |
5.1 |
| 13 | 2/22 | The matrix of a linear transformation - review. | 5.1, 5.2 |
| 14 | 2/27 | Coordinates of a vector. Changing coordinates. | 5.3, 5.4 |
| 15 | 3/1 | Matrices of a linear transformation. Similarity of matrices. |
5.3, 5.4 |
| 16 | 3/6 | Eigenvalues and eigenvectors - review. Diagonalizable matrices - review. Diagonalizable linear transformations. |
3.3 3.4 |
| 17 | 3/8 | Orthogonal diagonalization of real symmetric matrices. |
7.4 |
| - | 3/13-19 | -- Spring break -- | |
| 18 | 3/20 | Complex numbers. | 7.1 p. 401-408 |
| 19 | 3/22 | Complex numbers and complex vectors. | 7.1 p. 409-414 |
| 20 | 3/27 | Review. | |
| 21 | 3/29 | Exam 2 | |
| 22 | 4/3 | Exam 1 - discussion. Complex matrices. |
7.2 |
| 23 | 4/5 | Hermitian and unitary matrices. Mathematical induction. |
7.2 |
| 24 | 4/10 | Theorem of Shur. Spectral theorem. Principal axes theorem. |
7.3 |
| 25 | 4/12 | Normal matrices. Diagonalization - summary. |
7.3 |
| 26 | 4/17 | Jordan canonical form. | |
| 27 | 4/19 | Jordan canonical form. | |
| 28 | 4/24 | Jordan canonical form. | |
| 29 | 4/26 | Review |