Math 412: Advanced Linear Algebra

Fall Term 2019

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

Time Location Zoom Meeting ID Zoom Password
T 9:30-10:00 ORCH 3009 N/A N/A

Th 9:30-11:00 ORCH 3009 and on Zoom 694 6667 3745 914585

F 11:45-13:00 at PIMS and on Zoom 676 1308 4912 139267

Time	Location	Zoom Meeting ID	Zoom Password
T 9:30-10:00	ORCH 3009	N/A	N/A
Th 9:30-11:00	ORCH 3009 and on Zoom	694 6667 3745	914585
F 11:45-13:00	at PIMS and on Zoom	676 1308 4912	139267

Classes: TTh, 14:00-15:30 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 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

Roman, Advanced Linear Algebra, available from SpringerLink
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

Problem Sets

Solutions (only) are stored on a secure website; registered students can access them after first logging on to Canvas.
Problem set grade statistics.

Problem Set 1, due 12/9/2019. Solutions.
Problem Set 2, due 24/9/2019. Solutions.
Problem Set 3, due 1/10/2019. Solutions.
Problem Set 4, due 8/10/2019. Solutions.
Problem Set 5, due 15/10/2019. Solutions.
Problem Set 6, due 22/10/2019. Solutions.
Problem Set 7, due 5/11/2019. Solutions.
Problem Set 8, due 19/11/2019. Solutions.
Problem Set 9, due 19/11/2019. Solutions.
Problem Set 10, not for submission. Solutions.

For your edification

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

Week	Date	Material	Reading	Notes
1	Th 5/9	Introduction	§1,§2
2	T 10/9	Direct sum and product	§19,§20	Note on infinite dimensions
2	Th 12/9	(continued)		PS1 due
3	T 17/9	Quotients	§21,§22
3	Th 19/9	Duality	§13,§15
4	T 24/9	(continued) Bilinear forms	§23	PS2 due
4	Th 26/9	Tensor products	§24,§25
5	T 1/10	(continued)		PS3 due
5	Th 3/10	Extension of Scalars		Feedback form
6	T 8/10	\Sym^n and \wedge^n	§29,§30	PS4 due
6	Th 10/10	(continued)
7	T 15/10	Motivation The minimal polynomial	N2.1 N2.2	PS5 due
7	Th 17/10	Generalized eigenspaces	N2.3
8	T 22/10	Cayley--Hamilton	N 2.3	PS6 due
	Th 24/10	Jordan Blocks Nilpotent Jordan Form	§57, N 2.4
	T 29/10	Nilpotent Jordan form Jordan canonical form	§57, N 2.4 §58, N 2.5
9	Th 31/10	Vector Norms	§86, N 3.1
9	T 5/11	Matrix Norms Power Method	§87, N 3.2 N 3.3	PS7 due
10	Th 7/11	Completeness	N 3.4
10	T 12/11	Series	N 3.4
11	Th 14/11	Power series The Resolvent	N 3.5 N 3.6
11	T 19/11	Holomorphic calculus	N 3.7	PS8, PS9 due
12	Th 21/11	Composition	N 3.7
12	T 26/11			PS10 due
13	Th 28/11	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 11, 2019