# 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 (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
• 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

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

## 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.
1. Problem Set 1 (clarification added 17/1) (LyX, TeX), due 18/1/2021. Solutions.
2. Problem Set 2 (LyX, TeX), due 25/1/2021. Solutions.
3. Problem Set 3 (LyX, TeX), due 1/2/2021. Solutions.
4. Problem Set 4 (problem 5 fixed 4/2) (LyX, TeX), due 8/2/2021. Solutions.
5. Problem Set 5 (LyX, TeX), due 22/2/2021. Solutions.
6. Problem Set 6 (LyX, TeX), due 1/3/2021. Solutions.
7. Problem Set 7 (LyX, TeX), due 8/3/2021. Solutions.
8. Practice Problem Set 8 , not for submission. Solutions.
9. Problem Set 9 (LyX, TeX), (typos in problem 3(d),7(d) corrected; phrasing of problems 7,8 improved) due 22/3/2021. Solutions.
10. Problem Set 10 (LyX, TeX), due 29/3/2021. Solutions.
11. Problem Set 11 (LyX, TeX), due 7/4/2021. Solutions.
12. 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
F–I–S Axler
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

Back to my homepage.

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.