The applications of linear algebra are ubiquitous in both pure and applied math, and often underlie the methods and procedures utilized in a wide variety of domains. While the objects and methods of linear algebra are intrinsically interesting and fit into a rather elegant framework, these articles attempt to breathe a little modern life into them. My focus here is on intuition and motivation. As such, I take some liberties with the technical details of some of the applications. If these articles either provide useful analogies for how to think about these concepts or if they whet your appetite to dig in to the details of applications via a more robust and rigorous source, then I think they will have accomplished my goal in writing them.
These articles are not intended to teach the material of a linear algebra course, nor do they serve as a substitute for the work involved in completing such a course. I assume that you are either currently in an undergraduate course or have already completed such a course. As such, I take many concepts as familiar, and generally do not provide definitions, theorems, or proofs of these. At the moment, the topics used here match standard undergraduate material, with expansions hopefully to come in the near future.
Also, while I do not assume any programming background on your part, I have decided to leave the code that I have written to create these articles available for you. The format of the articles leaves code in clearly demarcated boxes that are interspersed throughout the article, and these may be safely skipped without affecting the flow of the commentary. That being said, I don’t think it is unfair to say that using math outside of academia generally involves a healthy amount of programming acumen. I think it would be slightly misleading to hide that reality from you, even in articles intended to accompany a pure math course. It is noteworthy that none of the code I have written is terribly complicated or sophisticated, and hopefully these articles give some indication as to how much can be accomplished with a little bit of familiarity (i.e., if you haven’t already, go learn a little programming).
Each of these articles contains a list of prerequisites and focuses on a, largely, self-contained application of some focused topic. As such, individual articles could be read in the order in which curiosity guides you. However, they were originally written as supplementary readings to a standard undergraduate course in linear algebra, and this gives them a natural order: