Syllabus (includes schedule).
Office hours: MW 1--3, TR 1--5 at LBV 321; email: david.milovich@tamiu.edu
| Day | Readings | Topics | Photos | Audio | Other | HW |
| 1 | 1A | introduction; Rn, Cn | zip | mp3 | 1A #10,11,16 | |
| 2 | 1B,C | vector spaces; subspaces | zip | mp3 | sums (jpeg) | 1B #2; 1C #12,20 |
| 3 | 2A | span; linear independence | zip | mp3 | 2A #10,15 | |
| 4 | 2B | bases | zip | mp3 (incomplete) |
2B #7 | |
| 5 | 2C | dimension | zip | mp3 | 1.43 solves 2C #17 | 2C #13,14 |
| 6 | 3A | linear transformations | zip | mp3 | summary (txt) | txt |
| 7 | 3B | null space and range | zip | mp3 | 3B #6,24 | |
| 8 | 3C | matrices | zip | mp3 | 3C #1,2 | |
| 9 | 3D | invertibility | zip | mp3 | 3D #4 (pdf) | 3D #6,7 |
| 10 | 3D | invertibility | zip | mp3 | left, right inverses (pdf) | 3D #8,13 |
| 11 | 3E | product and quotient spaces | zip | mp3 | ||
| 12 | 3F | dual spaces | zip | mp3 | 3F #32 | |
| 13 | 5A | eigenvalues, eigenvectors | zip | mp3 | 5A #10 | |
| 14 | 5B | existence of eigenvalues and upper triangular representations |
zip | mp3 | ||
| 15 | 5C | eigenspaces; diagonalization | zip | mp3 | 5C #16 | |
| 16 | 6A | inner product spaces | zip | mp3 | 6A #5,20 | |
| 17 | 6B | orthonormal bases | zip | mp3 | 6B #14 (jpeg) | 6B #6 |
| 19 | 6C | orthogonal complements | zip | mp3 | 6C #4,8 | |
| 20 | 7A | normal and self-adjoint operators | zip | mp3 | 7A #6,19 | |
| 21 | 7B | the Spectral Theorem | zip | mp3 | 7B #8,9 | |
| 22 | 7C | positive and isometric operators | zip | mp3 | 7C #4,7 | |
| 23 | 7D | polar and singular value decompositions | zip | mp3 | ||
| 24 | 8A | generalized eigenvectors | zip | mp3 (incomplete) |
Ch. 7 summary (pdf) | |
| 25 | 8A,B | nilpotent operators; a decomposition | zip | mp3 (incomplete) |
8B #6 | |
| 26 | 8B,C | operator decomposition; Cayley's Theorem | zip | mp3 | ||
| 28 | 8C,D | Jordan form; minimal and characteristic polynomials | zip | mp3 | ||
| 29 | 10 | trace and determinant | zip |
