Instructor: Johan Asplund, johan.asplund[at]stonybrook.edu, Office: Math Tower 3-116
Class time and location:
TR 12:30–1:50pm, Humanities 1006
Office hours:
TR 2:00–3:00pm (Math Tower 3-116) and W 5:00–6:00pm (by Zoom; email me)
Recitation 1: W 11:00–11:55am, Library E4315
TA: Junbang Liu, junbang.liu[at]stonybrook.edu
Office hours: W 2:00–3:00pm (Math Tower 2-118)
Recitation 2: W 11:00–11:55am, Mathematics 4-130
TA: Nate Tausik, nathan.tausik[at]stonybrook.edu
Office hours: W 2:00–3:00pm (Math Tower S-240A)
Recitation 3: W 11:00–11:55am, Mathematics P-131
TA: Ceyhun Elmacioglu, ceyhun.elmacioglu[at]stonybrook.edu
Office hours: W 2:00–3:00pm (Math Tower S-240A)
Syllabus: Here
Textbook: Linear Algebra Done Right (4th Edition) by Sheldon Axler (Free; pdf available here.)
Homework: Homework will be assigned weekly and is due the following Wednesday, as indicated in the tentative schedule below.
Gradescope: We will use Gradescope for assignment submission. Entry code: G3D77P
| Date | Topic | Read | HW | Due |
|---|---|---|---|---|
| Tue Jan 28 | Vector spaces | 1A, 1B (notes) | 1A: 4,9 1B: 3,7 1C: 1,12 |
W Feb 5 |
| Thu Jan 30 | Subspaces | 1C (notes) | ||
| Tue Feb 4 | Span and linear independence | 2A (notes) | 2A: 3,6,15 2B: 3,9 2C: 1,12 |
W Feb 12 |
| Thu Feb 6 | Bases and dimension | 2B, 2C (notes) | ||
| Tue Feb 11 | Linear maps | 3A | 3A: 1,4,7 3B: 1,6,13 |
W Feb 19 |
| Thu Feb 13 | Null space and range | 3B | ||
| Tue Feb 18 | Matrices | 3C | 3C: 1,3,10 3D: 2,9,11 |
W Feb 26 |
| Thu Feb 20 | Invertibility and isomorphisms | 3D | ||
| Tue Feb 25 | Products and quotients | 3E | None | |
| Thu Feb 27 | Duality | 3F | ||
| Tue Mar 4 | Midterm I (In class) | 4: 4,6,9 | W Mar 12 | |
| Thu Mar 6 | Polynomials | 4 | ||
| Tue Mar 11 | Invariant subspaces | 5A | 5A: 6,8,9 5B: 4,6,7 |
W Mar 26 |
| Thu Mar 13 | Minimal polynomial | 5B | ||
| Tue Mar 18 | No class (Spring Recess) | None | ||
| Thu Mar 20 | No class (Spring Recess) | |||
| Tue Mar 25 | Upper-triangular matrices | 5C | 5C: 1,9 5D: 2,3,13 |
W Apr 2 |
| Thu Mar 27 | Diagonalization | 5D | ||
| Tue Apr 1 | Commuting operators | 5E | 5E: 3 6A: 2,6,14 |
W Apr 9 |
| Thu Apr 3 | Inner products and norms | 6A | ||
| Tue Apr 8 | Orthonormal bases | 6B | None | |
| Thu Apr 10 | Orthogonal complements | 6C | ||
| Tue Apr 15 | Self-adjoint and normal operators | 7A | 6B: 2,8 6C: 2,3 |
W Apr 21 |
| Thu Apr 17 | Midterm II (In class) | |||
| Tue Apr 22 | Spectral theorem | 7B | 7A: 1,2 7B: 2,8 7C: 1,6 |
W Apr 30 |
| Thu Apr 24 | Positive operators | 7C | ||
| Tue Apr 29 | Isometries | 7D | 7D: 2,4 8A: 2,6,8 |
W May 7 |
| Thu May 1 | Generalized eigenvalues | 8A | ||
| Tue May 6 | Generalized eigenspace decomposition | 8B | None | |
| Thu May 8 | Jordan form | 8C | ||
| Thu May 15 | Final Exam: TBA | |||