Math 412: Advanced Linear Algebra

Fall Term 2017

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 (Fall 2024): after class (W 10:00-10:30 at the ESB atrium, W 14:00-14:30 at WW IRC Atrium), M 10:30-11:30 in my office, and by appointment.

Classes: TTh, 12:30-14:00 at GEOG 147.
Syllabus
(Rough) lecture notes

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

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

Midterm Exam

The exam will take place in-class on Thursday, October 19. The material for it is the "constructions" chapter of the course (lectures up to and including Thursday, October 5.
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.

Problem set grade statistics.

Problem Set 1, due 14/9/2017. Solutions.
Problem Set 2, due 21/9/2017 (typo in 5(b) corrected). Solutions (Solution to 5(a) fixed).
Problem Set 3, due 28/9/2017. Solutions.
Problem Set 4, due 5/10/2017. Solutions.
Problem Set 5, due 12/10/2017. Solutions.
Problem Set 6, due 26/10/2017. Solutions.
Problem Set 7, due 2/11/2017. Solutions.
Problem Set 8, due 9/11/2017. Solutions.
Problem Set 9, due 16/11/2017. Solutions (updated 6/12).
Problem Set 10, due 23/11/2017. Solutions (updated 6/12).

For your edification

Lecture-by-Lecture information

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

Week	Date	Material	Reading	Notes
1	Th 7/9	Introduction	§1,§2
2	T 12/9	Direct sum and product	§19,§20	Note on infinite dimensions
2	Th 14/9	(continued)		PS1 due
3	T 19/9	Quotients	§21,§22
3	Th 21/9	Duality	§13,§15	PS2 due
4	T 26/9	Bilinear forms Tensor Products	§23 §24,§25
4	Th 28/9	(continued)
5	T 3/10	\Sym^n and \wedge^n	§29,§30
5	Th 5/10	(continued)		PS4 due; Feedback form
6	T 10/10	Motivation The minimal polynomial	N2.1 N2.2
6	Th 12/10	Generalized eigenspaces	N2.3	PS5 due
7	T 17/10	Cayley--Hamilton Jordan Blocks	N 2.3 §57, N 2.4
7	Th 19/10	Midterm exam
8	T 24/10	Nilpotent Jordan form Jordan canonical form	§57, N 2.4 §58, N 2.5
8	Th 26/10	Vector Norms	§86, N 3.1	PS6 due
9	T 31/10	Matrix Norms Power Method	§87, N 3.2 N 3.3
9	Th 2/11	Completeness	N 3.4	PS7 due
10	T 7/11	Series	N 3.4
10	Th 9/11	Power series The Resolvent	N 3.5 N 3.6	PS8 due
11	T 14/11	Holomorphic calculus	N 3.7
11	Th 16/11	Composition	N 3.7	PS9 due
12	T 21/11
12	Th 23/11			PS10 due
13	T 28/11
13	Th 30/11	Review
	TBA	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 Wednesday December 06, 2017