Linear Algebra for CS559

in Math

Linear Algebra is essential for computer graphics. Here we describe some resources to help you get the basic intuitions. Either as a review, or if you’re learning it for the first time.

Linear algebra is essential for computer graphics. More specifically, having a good sense of the geometric intuitions behind basic linear algebra is critical for the foundations of graphics we need for introductory graphics (CS559).

A linear algebra class is not a pre-requisite for CS559 (as of Spring 2025). What we found, historically, is that most linear algebra classes are so focused on the mathematical abstractions that students need to learn (or at least review) the geometric intuitions of the basics.

Here are some resources to help you review (or learn, if you never have before) the basics of linear algebra focusing on their geometric intuitions.

Some of the things that are most essential in a linear algebra class (linear system solving, Gaussian Elimination, Eigenvalues, …) are less important for us.

Modern Resources

Most students prefer to learn from things other than traditional textbooks. So, we give these first.

Some ideas (please let us know if you have other suggestions):

  • The Three Blue One Brown Series on Linear Algebra - this is a series of YouTube videos (the link should be a playlist) that uses well-done animations to explain mathematical concepts. The focus here is more on the mathy abstractions than the geometric interpretations useful for graphics, but it is a lot more entertaining than reading a textbook.
  • Immersive Linear Algebra - this is an online textbook, which has the advantage that it is full of interactive (or at least animated) diagrams.

Regular Textbooks

In the past we recommended these two resources. They are both available online via the UW library. Copies of the key chapters are also in Canvas (for your section) in the “Files/Books” folder.

  • Practical Linear Algebra by Farin and Hansford. (UW Library Link - including to online) This is a book that teaches the basics of linear algebra by motivating it with geometric (graphics) examples. It is my top recommendation. We put copies of the key chapters in Canvas.
  • Chapter 5: Linear Algebra in Fundamentals of Computer Graphics. This chapter is a random assortment of explanations of linear algebra topics that are useful (for graphics in general). It is surprisingly disconnected from the geometric intuitions and uses in graphics.
  • The Appendix to the Real Time Rendering book has a quick review of the parts of linear algebra useful for graphics. It is online (and left out of the book!). It’s a good reminder of the equations and where they come from, but less good to learn it from in the first place.