Math 223: Linear Algebra

Winter Term 2020

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 (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: MWF, 10:00-10:50 on Zoom. If you are interested in attending lectures but aren't registered you can contact the instructor for the link.
Syllabus
(Rough) lecture notes
Canvas

References

Friedberg, Insel and Spence, Linear Algebra, Pearson.
Lipschutz, Schaum's Outline of Linear Algebra, McGraw-Hill.
Halmos, Finite-dimensional Vector Spaces, Springer.
Axler, Linear Algebra Done Right, Springer.

Exams

Midterm 1 will take place in class on Friday, February 5. Here is the pre-midterm information sheet. Here are the exam and a sample solution.
Midterm 2 will take place in class on Friday, March 12. Here are the exam and a sample solution.

Problem Sets

Problem sets are due at 10:00 Vancouver time (start of class) on the date indicated. We expect typeset solutions.
- Two options include installing LyX to your computer or using Overleaf online.
- Here are some notes on LaTeX from a past MATH 220 instructor, which include links to further information.
- The source files for the problem sets rely on my macro file. Feel free to use it for you submissions as well.
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 (clarification added 17/1) (LyX, TeX), due 18/1/2021. Solutions.
Problem Set 2 (LyX, TeX), due 25/1/2021. Solutions.
Problem Set 3 (LyX, TeX), due 1/2/2021. Solutions.
Problem Set 4 (problem 5 fixed 4/2) (LyX, TeX), due 8/2/2021. Solutions.
Problem Set 5 (LyX, TeX), due 22/2/2021. Solutions.
Problem Set 6 (LyX, TeX), due 1/3/2021. Solutions.
Problem Set 7 (LyX, TeX), due 8/3/2021. Solutions.
Practice Problem Set 8 , not for submission. Solutions.
Problem Set 9 (LyX, TeX), (typos in problem 3(d),7(d) corrected; phrasing of problems 7,8 improved) due 22/3/2021. Solutions.
Problem Set 10 (LyX, TeX), due 29/3/2021. Solutions.
Problem Set 11 (LyX, TeX), due 7/4/2021. Solutions.
Problem Set 12 (LyX, TeX), due 14/4/2021. Solutions.

Lecture-by-Lecture information

We give section numbers in the textbook [1]; page numbers in the textbook [4]. A precis of the material also appears in the course notes.

Warning: the following information is tentative and subject to change at any time

Week	Date	Material	Reading		Scan	Notes
Week	Date	Material	F–I–S	Axler	Scan	Notes
1	M 11/1	Introduction: Linearity			Scan	slides handout
	W 13/1	Vector spaces	§1.2	pp. 4-12	Scan
	F 15/1	Subspaces	§1.3	p. 13	Scan
2	M 18/1	Linear combinations	§1.4	p. 22	Scan	PS1 due
	W 20/1	Linear independence	§1.5	pp. 22-27	Scan
	F 22/1	Bases	§1.6	pp. 27-31	Scan
3	M 25/1	Dimension		pp. 31-34	Scan	PS2 due
	W 27/1	Geometry			Scan
	F 29/1	Linear maps	§2.1	pp. 37-41	Scan
4	M 1/2	Kernel and image		pp. 41-47	Scan	PS3 due
	W 3/2	Matrices	§2.2	pp. 48-50	Scan
	F 5/2	Midterm 1				Info
5	M 8/2	Midterm review			Scan	PS4 due
	W 10/2	Matrix multiplication	§2.3	pp. 50-53	Scan
	F 12/2	Linear equations	§3.3		Scan
6	M 22/2	Gaussian Elimination	§3.1, §§3.3-4		Scan	PS5 due
	W 24/2	(continued)			Scan
	F 26/2	Determinants	§§4.1-3	pp. 225-236	Scan
7	M 1/3	(continued)			Scan	PS6 due
	W 3/3	Determinants, Again	§4.5		Scan
	F 5/3	(continued)			Scan
8	M 8/3	Similarity	§2.5		Scan	PS7 due
	W 10/3	Eigenvalues	§5.1	pp. 75-79	Scan
	F 12/3	Midterm 2
9	M 15/3	Midterm review			Scan	(no PS8)
	W 17/3	Multiplicity			Scan
	F 19/3	Multiplicity		pp. 87-90	Scan
10	M 22/3	Diagonalization	§5.2		Scan	PS9 due
	W 24/3	Application			Scan
	F 26/3	Inner product spaces	§6.1	Ch. 6	Scan
11	M 29/3	Cauchy--Schwartz			Scan	PS10 due
	W 31/3	Gram--Schmidt			Scan
	W 7/4	Orthogonality			Scan	PS11 due
12	F 9/4	The Adjoint	§6.4	pp. 127-137	Scan
	M 12/4	The Spectral Theorem			Scan
	W 14/4	(continued)			Scan	PS12 due
	W 29/4	Final Exam: 8:30am-11am

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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 Monday April 26, 2021