# Math 223: Linear Algebra

Winter Term 2021
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. 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.

## Exams

• Midterm 1 will take place in class on Monday, February 7. Here is the pre-midterm information sheet.
• Midterm 2 will take place in class on Friday, March 11. Here is the pre-midterm information sheet.

## Problem Sets

• Problem sets are due at 10:00 Vancouver time (start of class) on the date indicated. Submission is on Canvas, and 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 (LyX, TeX), due 20/1/2022 (questions 1(b),3,5 clarified). Solutions.
2. Problem Set 2 (LyX, TeX), due 26/1/2022 (typos in 4(b),4(d) fixed). Solutions.
3. Problem Set 3 (LyX, TeX), due 2/2/2022. Solutions.
4. Problem Set 4 (LyX, TeX), due 9/2/2022. Solutions.
5. Problem Set 5 (LyX, TeX), due 16/2/2022 (minor typos fixed). Solutions.
6. Problem Set 6 (LyX, TeX), due 1/3/2022. Solutions.
7. Problem Set 7 (LyX, TeX), due 7/3/2022. Solutions.
8. Problem Set 8 (LyX, TeX), due 14/3/2022. Solutions.
9. Problem Set 9 (LyX, TeX), due 21/3/2022. Solutions.
10. Problem Set 10 (LyX, TeX), due 28/3/2022 (question 2(d) removed, 2(c) adjusted; more typos fixed). Solutions.
11. Problem Set 11 (LyX, TeX), due 4/4/2022 (typo in 2(a) fixed). Solutions.
12. Problem Set 12 (LyX, TeX), due 11/4/2022. Solutions.

## Lecture-by-Lecture information

It is crucial to read the relevant material ahead of each lecture in order to properly participate and learn. The goal is not to master the material but to learn the new vocabulary and see how the concepts hang together.

The table gives section numbers in the textbook [1] and page numbers in the textbook [4], but you should feel free to read any book on the topic. 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 Recap Notes
F–I–S Axler
1 M 10/1 Introduction: Linearity     Scan slides handout
W 12/1 Vector spaces §1.2 pp. 4-12 Scan
F 14/1 Subspaces §1.3 p. 13 Scan
2 M 17/1 Linear combinations §1.4 p. 22 Scan
Video
PS1 due
W 19/1 Linear independence §1.5 pp. 22-27 Scan
F 21/1 Bases §1.6 pp. 27-31 Scan
3 M 24/1 Dimension   pp. 31-34 Scan
W 26/1 Geometry     Scan PS2 due
F 28/1 Linear maps §2.1 pp. 37-41 Scan
4 M 31/1 Kernel and image   pp. 41-47 Scan
W 2/2 Matrices §2.2 pp. 48-50 Scan PS3 due
F 4/2 Matrix multiplication §2.3 pp. 50-53 Scan
5 M 7/2 Midterm 1   Info
W 9/2 Midterm review     PS4 due
F 11/2 Linear equations §3.3
6 M 14/2 Gaussian Elimination §3.1, §§3.3-4
W 16/2 (continued)     PS5 due
F 18/2 Determinants §§4.1-3 pp. 225-236
21/2-27/2 Midterm break
7 M 28/2 (continued)     PS6 due
W 2/3 Determinants, Again §4.5
F 4/3 (continued)
8 M 7/3 Similarity §2.5   PS7 due
W 9/3 Eigenvalues §5.1 pp. 75-79
F 11/3 Midterm 2
9 M 14/3 Midterm review     PS8 due
W 16/3 Multiplicity
F 18/3 Multiplicity   pp. 87-90
10 M 21/3 Diagonalization §5.2   PS9 due
W 23/3 Application
F 25/3 Inner product spaces §6.1 Ch. 6
11 M 28/3 Cauchy--Schwartz     PS10 due
W 30/3 Gram--Schmidt
F 1/4 Orthogonality
12 M 4/4 The Adjoint §6.4 pp. 127-137 PS11 due
W 6/4 The Spectral Theorem
F 8/4 (continued)
M 11/4 no lecture PS12 due
W 27/4 Final Exam: LIFE 2212

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