This is course about vector spaces and linear transformations. It is not a course about vectors, in the sense of lists of numbers, and matrices (for this see Math 220), although we will of course make use of these concepts as needed. This course has a theoretical bent: we want to understand vector spaces and linear transformations, rather than use them to solve specific problems. For a more applied, engineering-oriented approach, try Math 441. This is a mathematics class, and you will be expected to read and do proofs.

Students come to this class with a range of backgrounds. Some are very well prepared, while some will need to fill in needed background (e.g. fields, polynomials) as we go. If you find yourself in the second group, rest assured that I will provide some of this material as we go, although you should expect to spend some extra time getting caught up.

Instructor: Jason R. Morton, Assistant Professor, 219B McAllister Building. Email: morton@math.psu.edu.

Online discussion: Rather than emailing questions to myself or the TA, I encourage you to post your questions on our online forum. You are encouraged to answer other’s questions as well!

Prerequisites: Math 311W, providing background on reading and writing proofs, the axiomatic approach, groups and fields, and a little linear algebra. Familiarity with linear algebra at the level of Math 220 may be helpful, but is not required.

Course description: Vector spaces and linear transformations, canonical forms of matrices, inner products, invariant properties; applications. This is a second course in linear algebra, and emphasizes proofs and an abstract point of view (understanding vector spaces and linear transformations, not manipulating lists and matrices of numbers). We build up to and use structure theorems for linear operators.

Text: Linear Algebra Done Right (3rd Edition), by Sheldon Axler. We will cover most of the book, as well as a few supplementary topics. You are encouraged to look at other sources of information and books at your discretion.

Video lectures to accompany these notes are available.