This is a second course in linear algebra, intended for honours students. There is no required textbook. The book by Halmos is very good, covers nearly everything, and is available in PDF form from the publisher for anyone on the UBC network; a lot of the material can also be found in any "abstract algebra" textbook. More details may be found in the syllabus.
Section numbers marked § are in Halmos [1], section numbers marked N are in the course notes above.
| Week | Date | Material | Reading | Notes |
|---|---|---|---|---|
| 1 | M 6/1 | Introduction | §1,§2 | |
| W 8/1 | Direct sum and product | §19,§20 | Note on infinite dimensions | |
| F 10/1 | (continued) | |||
| 2 | M 13/1 | (continued) | ||
| W 15/1 | Quotients | §21,§22 | PS1 due | |
| F 17/1 | Duality | §13,§15 | ||
| 3 | M 20/1 | (continued) | ||
| W 22/1 | (continued) | PS2 due | ||
| F 24/1 | Billinear forms | §23 | ||
| 4 | M 27/1 | Tensor products | §24,§25 | Note on categories |
| W 29/1 | (continued) | PS3 due | ||
| F 31/1 | Review | |||
| 5 | M 3/2 | \Sym^n and \wedge^n | §29,§30 | |
| W 5/2 | (continued) | |||
| F 7/2 | Motivation | PS4 due; Feedback form | ||
| 6 | W 12/2 | The minimal polynomial | N 2.2.1 | |
| F 14/2 | Generalized eigenspaces | N 2.2.2 | PS5 due | |
| M 24/2 | Midterm exam | |||
| 7 | W 26/2 | Algebraic closure | N 2.2.3 | |
| F 28/2 | Nilpotence | N 2.2.4 | PS6 due | |
| 8 | M 3/3 | Jordan blocks | N 2.2.4 | |
| W 5/3 | Nilpotent Jordan form | N 2.2.4 | ||
| F 7/3 | Jordan canonical form | N 2.2.5 | ||
| 9 | M 10/3 | Vector Norms | §86, N 3.1 | PS7 due |
| W 12/3 | Matrix Norms | §87, N 3.2 | ||
| F 14/3 | (continued) | |||
| 10 | M 17/3 | Power method | ||
| W 19/3 | Completeness | PS8 due | ||
| F 21/3 | Series | |||
| 10 | M 24/3 | Power series | ||
| W 26/3 | Holomorphic calculus | PS9 due | ||
| F 28/3 | Composition | |||
| 12 | M 31/3 | The Resolvent | ||
| W 2/4 | ||||
| F 4/4 | ||||
| 13 | M 7/4 | Review | PS10 due | |
| M 16/4 | Final exam |
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Clarification: the writings on these pages are generally my own creations (to which I own the copyright), and are made available for traditional academic reuse. If you wish to republish substantial portions (including in "derivative works") please ask me for permission. The material is expressly excluded from the terms of UBC Policy 81.
Last modified Friday May 02, 2014