| Spring 2024 MAT 310: Linear algebra | ||
| Schedule | TuTh 2:30-3:50pm Humanities 1003 | |
| Instructor | Robert Hough | |
| Office hours | F 1-2pm in Math Learning Center, F 2-4pm in Math Tower 4-118 | |
| TAs | Shuhao Li , Alessandro Pilastro and Joao Pering | |
| Description | Finite dimensional vector spaces, linear maps, dual spaces, bilinear functions, inner products. Additional topics such as canonical forms, multilinear algebra, numerical linear algebra. | |
| Prerequisites | C or higher in MAT 211 or 305 or 308 or AMS 210; C or higher in MAT 200 or MAT 250 or permission of instructor | |
| Textbook | Linear Algebra Done Right (4th edition) by Sheldon Axler. The textbook is available free online at https://link.springer.com/book/10.1007/978-3-031-41026-0. | |
| Homework | Weekly problem sets will be assigned, and collected in recitation. Late homework is not accepted, but under documented extenuating circumstances the grade may be dropped. Your lowest homework grade will be dropped at the end of the class. | |
| Grading | Homework: 20%, Midterm I: 20%, Midterm II: 20%, Final: 40%. | |
Accommodations for students with hearing and communication impairments:
Some students with hearing and communication impairments may need their instructor to wear a
clear mask for lip and facial expression purposes. If the student has registered with the Student
Accessibility Support Center (SASC) and has requested an accommodation for clear masks, SASC
will reach out to the students instructors and provide a clear mask for them to wear while teaching
and/or interacting with the student. If you have questions, please email sasc@stonybrook.edu or
call (631) 632-6748.
Syllabus/schedule (subject to change)
| Tue 1/23 | 1. | R^n, C^n, definition of vector space | 1A-1B |
| Thu 1/25 | 2. | Subspaces | 1C Week 1 HW: 1A 9, 10, 15 1B 3, 7 1C 3, 4, 22 |
| Tue 1/30 | 3. | Span, Linear independence | 2A |
| Thu 2/1 | 4. | Bases, dimension | 2B-2C Week 2 HW: 2A 3, 9, 19 2B 7, 9, 10 2C 3, 4, 20 |
| Tue 2/6 | 5. | Vector space of linear maps, null space, range | 3A-3B |
| Thu 2/8 | Midterm 1 | Week 3 HW: 3A 3, 7, 12, 15 3B 3, 10, 22, 25 | |
| Tue 2/13 | 6. | Matrices, inverses and isometries | 3C-3D |
| Thu 2/15 | 7. | Products, quotient vector spaces | 3E Week 4 HW: 3C #3, 5, 17 3D #2, 8, 16 3E #1, 4, 13, 17 |
| Tue 2/20 | 8. | Duality | 3F |
| Thu 2/22 | 9. | Zeros of polynomials, division algorithm for polynomials | 4A-4B Week 5 HW: 3F #5, 7, 8 4 #6, 7, 10, 13, 14 |
| Tue 2/27 | 10. | Factorization of polynomials | 4C-4D |
| Thu 2/29 | 11. | Invariant subspaces | 5A Week 6 HW: 5A #2, 8, 13, 15, 20, 38 |
| Tue 3/5 | 12. | Minimum polynomial | 5B |
| Thu 3/7 | 13. | Upper triangular matrices | 5C Week 7 HW: 5B #4, 9, 10, 15 5C #3, 7, 12, 14 |
| 3/11-3/15 | Spring break | ||
| Tue 3/19 | 14. | Diagonalizable operators, commuting operators | 5D-5E |
| Thu 3/21 | 15. | Inner products, norms | 6A Week 8 HW: 5D #2, 3, 4, 8 5E #3, 6, 10 6A #1, 2, 6, 10, 14 |
| Tue 3/26 | 16. | Orthonormal bases | 6B |
| Thu 3/28 | 17. | Orthogonal complement, minimization | 6C Week 9 HW: 6B #1, 4, 7, 9 6C #4, 5, 12, 20 |
| Tue 4/2 | Midterm 2 | ||
| Thu 4/4 | 18. | Self-adjoint operators, normal operators | 7A Week 10 HW: 7A #3, 5, 7, 27, 31 |
| Tue 4/9 | 19. | Spectral theorem | 7B |
| Thu 4/11 | 20. | Positive operators, isometry | 7C-7D Week 11 HW: 7B #3, 8, 13, 23 7C #5, 6, 10 7D #8, 10, 19 |
| Tue 4/16 | 21. | Singular value decomposition | 7E |
| Thu 4/18 | 22. | Generalized eigenvalues, nilpotent operators | 8A Week 12 HW: 7E #7, 8, 10, 14 8A #2, 4, 6, 17, 22 |
| Tue 4/23 | 23. | Generalized eigenspace decomposition | 8B-8C |
| Thu 4/25 | 24. | Trace, quadratic forms | 8D, 9A Week 13 HW: 8B #3, 8, 10, 18 8C #7, 11, 13 8D #2, 11 9A #6, 8, 9 |
| Tue 4/30 | 25. | Alternating multilinear forms, determinants | 9B-9C |
| Thu 5/2 | 26. | Tensor product | 9D |
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