Summary
Online course in abstract linear algebra (rigorous, proof-based).
This page serves as a resource to my online asynchronous course on Abstract Linear Algebra. The YouTube playlist is here: https://www.youtube.com/playlist?list=PLoxJTbDttvt7ny0WEJHWw6-0Sjx7EImIQ
Originally, this course was taught in summer 2020 at the University of Washington. It serves as a second course in linear algebra, with all of the students having taken an introductory course in linear algebra which was more computational in nature. Nevertheless, the mathematically mature student could take this as a first course in linear algebra. The most recent version of Axler’s textbook, Linear Algebra Done Right is now available free on his website: https://linear.axler.net/
Linear algebra is an incredibly powerful subject which is used throughout mathematics, statistics, engineering, computer science, data science, machine learning, and economics. If it feels like I am overstating the power of linear algebra, I would say it is more likely that I’m understating it—there are far more applications of linear algebra than I have time to understand. If you can understand linear algebra conceptually, computationally, and geometrically, then you will be able to use it in whatever application you care most about!
Together with the free textbook, the free YouTube playlist, and the free course materials posted below, I hope that you are able to learn linear algebra in a deep conceptual way no matter your age, location, job, interests, or state in life.