This is a second course in linear algebra, intended for honours students. There is no required textbook. The books by Roman and Halmos are both very good, cover most of the material, and are 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.
For your edification
Section numbers marked § are in Halmos [2], section numbers marked N are in the course notes above.
Warning: the following information is tentative and subject to change at any time
| Week | Date | Material | Reading | Notes |
|---|---|---|---|---|
| 1 | M 9/1 | Introduction | §1,§2 | |
| W 11/1 | External direct sum | §19,§20 | Note on infinite dimensions | |
| F 13/1 | Internal direct sum | |||
| 2 | M 16/1 | Direct sums | ||
| W 18/1 | Abstract direct sum | PS1 due | ||
| F 20/1 | Quotients | §21,§22 | ||
| 3 | M 23/1 | Duality | §13,§15 | |
| W 25/1 | (continued) | PS2 due | ||
| F 27/1 | Bilinear forms | §23 | ||
| 4 | M 30/1 | Tensor products | §24,§25 | |
| W 1/10 | (continued) | Feedback form | ||
| F 3/10 | Examples | PS3 due | ||
| 5 | M 6/2 | Tensor powers | ||
| W 8/2 | \Sym^n and \wedge^n | §29,§30 | ||
| F 10/2 | (continued) | PS4 due | ||
| 6 | M 13/2 | (continued) | ||
| W 15/2 | The determinant | |||
| F 17/2 | Motivation | PS5 due | ||
| 7 | M 27/2 | Midterm Exam | ||
| W 1/3 | The minimal polynomial | N2.1 N2.2 |
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| F 3/3 | Generalized eigenspaces | N2.3 | PS6 due | |
| 8 | M 6/3 | (continued) | ||
| W 8/3 | Cayley--Hamilton | N 2.3 | ||
| F 10/3 | Jordan Blocks | §57, N 2.4 | PS7 due | |
| 9 | M 13/3 | Nilpotent Jordan form | §57, N 2.4 | |
| M 15/3 | Jordan canonical form | §58, N 2.5 | ||
| F 17/3 | (continued) | PS8 due | ||
| 10 | M 20/3 | Vector Norms | §86, N 3.1 | |
| W 22/3 | Matrix Norms | §87, N 3.2 | ||
| F 24/3 | The power method | N 3.3 | PS9 due | |
| 11 | M 27/3 | Completeness | N 3.4 | |
| W 29/3 | Series | N 3.4 | ||
| F 31/3 | Power series | N 3.5 | ||
| 12 | M 2/4 | The Resolvent | N 3.6 | |
| W 4/4 | Holomorphic calculus | N 3.7 | PS10 due | |
| F 11/4 | Composition | |||
| F 21/4 | Final exam: 12:00-14:30 BUCH B209 | |||
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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 Wednesday April 05, 2023