MAT 3141 (Fall 2012)

Linear Algebra II

About The Course

This is a second course in abstract linear algebra. It will combine ideas from MAT 2141 on linear algebra over fields with concepts from MAT 2143 (in particular, groups and rings). We will see many useful concepts such as modules, dual spaces (introduced in MAT 2141), and tensor products that are ubiquitous in mathematics (and physics).

Official Course Description

Finitely generated modules over a Euclidean domain, equivalence of matrices, the rational and Jordan canonical form, the Cayley-Hamilton Theorem, spectral theorems, linear functionals, dual spaces, tensor products.

Prerequisites

MAT 2141 (Linear Algebra I), MAT 2143 (Algebraic Structures).

Course Text

This course has no official textbook. Course notes will be made available to students electronically on the syllabus page.

MAT 3541 course notes: These are excellent notes for the French version of this course (MAT 3541), written by Damien Roy. We will follow these notes quite closely for most of the course. As the course progresses, English versions of these notes will be posted on the syllabus page.

Students looking for additional references are advised to look at the following texts. Both are on reserve at Morisset Library.

  • Sterling K. Berberian, Linear Algebra, Oxford University Press, 1992. This text has been used for MAT 2141 in the past. It is currently out of print, but the author has been kind enough to grant permission for students in this course to purchase a photocopy. Students who do not have it can purchase a photocopy for $24.14 at the docUcentre, Room 0024, University Centre.
  • Serge Lang, Linear Algebra, Third Edition, Springer, 1987. ISBN: 978-0387964126 (or the 2010 paperback version, ISBN 978-1441930811). Interested students can purchase it online. Hardcover: Chapters, Amazon. Paperback: Chapters, Amazon.

MAT 2141 course notes: Students looking to refresh their memory on material from MAT 2141 can download the instructor's notes for that course.

Course Outline

A more detailed syllabus can be found here.

Course Webpage

There are two main online locations for information regarding the course:

  • https://alistairsavage.ca/mat3141. This is the course home page. It will be updated regularly and contains important material for the course. Announcements will also be posted here.
  • Virtual Campus. Students can access their grades via Virtual Campus.