Winter Term 2021

Lior Silberman
- 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

- 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

- 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.

- 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 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**. - Problem set grade statistics.

- Problem Set 1 (LyX, TeX), due 20/1/2022 (questions 1(b),3,5 clarified). Solutions.
- Problem Set 2 (LyX, TeX), due 26/1/2022 (typos in 4(b),4(d) fixed). Solutions.
- Problem Set 3 (LyX, TeX), due 2/2/2022. Solutions.
- Problem Set 4 (LyX, TeX), due 9/2/2022. Solutions.
- Problem Set 5 (LyX, TeX), due 16/2/2022 (minor typos fixed). Solutions.
- Problem Set 6 (LyX, TeX), due 1/3/2022. Solutions.
- Problem Set 7 (LyX, TeX), due 7/3/2022. Solutions.
- Problem Set 8 (LyX, TeX), due 14/3/2022. Solutions.
- Problem Set 9 (LyX, TeX), due 21/3/2022. Solutions.
- Problem Set 10 (LyX, TeX), due 28/3/2022 (question 2(d) removed, 2(c) adjusted; more typos fixed). Solutions.
- Problem Set 11 (LyX, TeX), due 4/4/2022 (typo in 2(a) fixed). Solutions.
- Problem Set 12 (LyX, TeX), due 11/4/2022. Solutions.

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 |

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.