## Overview

In this course, we will take a more abstract approach to linear algebra than the one taken in MAT 1341 (the prerequisite for this course). Instead of working only with real or complex numbers, we will generalize to the setting where our coefficients lie in a field. The real numbers and complex numbers are both examples of fields, but there are others as well. We will revisit familiar topics such as matrices, linear maps, determinants, and diagonalization, but now in this more general setting and at a deeper level. We will also discuss more advanced topics such as dual spaces, multilinear maps, and inner product spaces. Compared to MAT 1341, this course will concentrate more on justification of results and mathematical rigour as opposed to computation. Almost all results will be accompanied by a proof and students will be expected to do proofs on assignments and exams.

### MAT 2141 versus MAT 2342

MAT 2342 (and its French equivalent MAT 2742) covers similar material to MAT 2141 (and its French equivalent MAT 2541) but is more applied and less abstract, and aimed at students studying economics or statistics. Depending on their program, students may have the option of taking either MAT 2141 or MAT 2342. Students in the MAT-ECON or FIN-MAT-ECO programs and in statistics are especially encouraged to take MAT 2342 instead of MAT 2141. Students considering graduate studies in mathematics are encouraged to take MAT 2141. If you're unsure of which course you should be taking, you can discuss your options with the professor.

## Official course description

Vector spaces, direct sums and complement of subspaces, linear maps, representation of linear maps by matrices, dual spaces, transpose mappings, multilinear mappings, determinants, inner products, orthogonal projections, the Gram-Schmidt algorithm. Eigenvalues and eigenvectors, diagonalization of symmetric matrices. The emphasis of this course is on proving all results.

## Prerequisites

MAT 1341, (MAT 1348 or MAT 1362 or MAT 2362).

## Reference material

### Lecture notes

Click the above header to download lecture notes for the course. They are a single file that may be updated as the course progresses. They should be complemented by your own class notes. I will often say more in class than is in the lecture notes.

### Textbook

Sergei Trei, Linear Algebra Done Wrong. This is an open access textbook that covers most of the topics of MAT 2141. The webpage for this book can be found here.

### Optional additional reference

Sterling K. Berberian, *Linear Algebra*. ISBN-13: 978-0486780559. Since this is not a required textbook, it is not available at the university bookstore. Inexpensive electronic or print versions can be ordered online.

## DGDs

The DGDs are an important part of the course. They are led by the professor and supplement the material covered in the lectures. In the DGDs, you will be given an opportunity to ask questions about the lectures. In addition, we will go through the recommended exercises that correspond to the lectures from the past week. To get the most from the DGDs, you **should attempt the recommended exercises before the DGDs**. That way, you can focus on clearing up any difficulties that you encounter. Graded quizzes and tests will also be handed back in the DGDs.

## Extra help

The Math Help Centre does not serve this course. However, if you are looking for extra help beyond the DGDs and office hours, you can hire a private tutor using the tutor referral service of the Peer Help Centre.

## Course website

There are two main locations for information regarding the course:

- alistairsavage.ca/mat2141/. This is the main course website. It will be updated regularly and contains important material for the course.
- Brightspace. Assignments will be submitted on Brightspace. This is also where grades will be posted.