Winter Term 2023
Lior Silberman

General Information

• Office: MATX 1112, 604-827-3031
• Email: "lior" (at) Math.UBC.CA (please include the course number in the subject line, if applicable)
• Office hours (Winter 2024): by appointment or
T 9:30-10:00ORCH 3009N/AN/A
Th 9:30-11:00ORCH 3009 and on Zoom694 6667 3745914585
F 11:45-13:00at PIMS and on Zoom676 1308 4912139267

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.

References

2. Halmos, Finite-dimensional Vector Spaces, available from SpringerLink
3. Coleman, Calculus on Normed Vector Spaces, Chapter 1 (on SpringerLink)
4. Higham, Functions of Matrices, available from SIAM
5. [Your favorite author], Abstract Algebra

Midterm Exam

• The exam will take place in-class on Monday, Feburary 27. The material for it is the "constructions" chapter of the course (lectures up to and including Wendesday, Feburary 15).
• Here is a previous midterm.
• Here is this year's midterm (restricted to students in the course).

Problem Sets

• Problem sets are due at 10:00 Vancouver time (start of class) on the date indicated. Submission is on Canvas, and I expect typeset solutions.
• The source files for the problem sets rely on my macro file. Feel free to use it for your submissions as well.
• Solutions (only) are stored on a secure website; registered students can access them after first logging on to Canvas.
1. Problem Set 1 (LyX, TeX), due 18/1/2023. Solutions
2. Problem Set 2, (LyX, TeX), due 25/1/2023. Solutions.
3. Problem Set 3, due 3/2/2023.
4. Problem Set 4, due 10/2/2023.
5. Problem Set 5, (LyX, TeX), due 17/2/2023.
6. Problem Set 6, (LyX, TeX), due 22/10/2019.
7. Problem Set 7, due 10/3/2023.
8. Problem Set 8, due 17/3/2023.
9. Problem Set 9 (LyX, TeX), due 24/3/2023.
10. Problem Set 10: Q2b corrected (LyX, TeX),

Lecture-by-Lecture information

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

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

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.