# Math 412: Advanced Linear Algebra

Fall Term 2016
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: by appointment

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.

## References

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

## Final Exam

• The exam will take place Tuesday, Decenber 6 between 8:30-11:30 in Geography 214.
• Here is a previous exam in this course.

## Midterm Exam

• The exam will take place in-class on Wednesday, October 19. The material for it is the "constructions" chapter of the course (lectures up to and including Friday, October 7.
• Here is a previous midterm.
• Here are this year's midterm and its solution (both links restricted to students in the course).

## Problem Sets

• Solutions (only) are stored on a secure website; registered students can access them after first logging on to Connect.
• (both links restricted to students in the course).
1. Problem Set 1, due 14/9/2016. Solutions.
2. Problem Set 2, due 21/9/2016. Solutions.
3. Problem Set 3, due 28/9/2016 (added practice problem, clarification on P4, hint to 1(a)) Solutions.
4. Problem Set 4, due 5/10/2016. Solutions.
5. Problem Set 5, due 12/10/2016. Solutions.
6. Problem Set 6, due 26/10/2016 (problem 2(c) clarified). Solutions.
7. Problem Set 7, due 2/11/2016. Solutions.
8. Problem Set 8, due 9/11/2016. Solutions.
9. Problem Set 9, due 16/11/2016. Solutions.
10. Problem Set 10, now due 30/11/2016. Solutions.

## Lecture-by-Lecture information

Section numbers marked § are in Halmos [1], section numbers marked N are in the course notes above.

1 W 7/9 Introduction §1,§2
F 9/9 Direct sum and product §19,§20 Note on infinite dimensions
2 M 12/9 (continued)
W 14/9 (continued)   PS1 due
F 16/9 Quotients §21,§22
3 M 19/9 Duality §13,§15
W 21/9 (continued)   PS2 due
F 23/9 (continued)
4 M 26/9 Bilinear forms §23
W 28/9 Tensor products §24,§25 PS3 due, Note on categories
F 30/9 (continued)
5 M 3/10 (continued)
W 5/10 \Sym^n and \wedge^n §29,§30 PS4 due; Feedback form
F 7/10 (continued)
6 W 12/10 Motivation   PS5 due
F 14/10 The minimal polynomial N 2.2
7 M 17/10 Generalized eigenspaces N 2.3
W 19/10 Midterm exam
F 21/10 Cayley--Hamilton N 2.3
8 M 24/10 Jordan Blocks §57, N 2.4
W 26/10 Nilpotent Jordan form §57, N 2.4 PS6 due
F 28/10 Jordan canonical form §58, N 2.5
9 M 31/10 Vector Norms §86, N 3.1
W 2/11 Matrix Norms §87, N 3.2 PS7 due
F 4/11 (continued)
10 M 7/11 Power method N 3.3
W 9/11 Completeness N 3.4 PS8 due
11 M 14/11 Series N 3.4
W 16/11 Power series N 3.5 PS9 due
F 18/11 The Resolvent N 3.6
12 M 21/11 Holomorphic calculus N 3.7
W 23/11 Composition N 3.7 PS10 due
F 25/11
13 M 28/11
W 30/11     PS10 due
F 2/12 Review
T 6/12 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.