In the past weeks, I have been studying Linear Algebra and encountered many valuable resources along the way. This article aims to provide you with a complete (yet concise!) guide to get you started right away.
Why Learn Linear Algebra?
Linear Algebra is essential in various fields such as computer science, machine learning and physics. This first answer on Stack Exchange sums it up nicely, for those looking for a more extensive explanation.
The Master Plan
Part 1 — Exercises & Problem Solving
As main resource I used Brilliant.org, a platform that teaches problems and courses in mathematics, computer science, physics and quantitive finance. While learning about the subject at hand, the focus lies on improving your problem solving skills. Don’t expect the problems to be easy — they are meant to encourage you to think about the materials and require you to have truly understood them in order to answer the quizzes correctly. You can tell the people from Brilliant are passionate about what they do by looking at the problems and their educators page.
As a rule of thumb, I always work on the problem for 20 minutes without other resources or help. If I haven’t gotten the answer yet after these 20 minutes, I will use google to get to the answer or check the solution.
The second main resource I used is “The Manga Guide to Linear Algebra”, which is essentially a comic book that explains Linear Algebra. It’s a very fun read and it explains the concepts in an intuitive manner.
Part 2 — Intuition
While some of you may already be familiar with this channel, the absolute best way to understand the intuition behind Linear Algebra is “The Essence of Linear Algebra” series from the youtube channel 3Blue1Brown. Grant explains the concepts in a very elegant and clear way. I watched some videos multiple times, just to really reinforce the intuition in my brain.
(I am not sure whether it is a collaboration, but the series seems to align perfectly with the Brilliant course.)
Part 3— Extra Guidance and Explanation
For additional resources, there are three that I found particularly useful.
- Obviously, Khan Academy’s series on Linear algebra. There is a video explaining and going through examples of (almost) every concept you may want to know more about.
- Math is fun is famous for explaining mathematical concepts in the simplest form possible. Googling the concept + Math is fun will get you there.
- The Brilliant wiki page on Linear algebra also has lots of additional information. Sometimes they go a bit more in depth or cover slightly different things than in the quizzes.
And that’s it! Hopefully this will help you getting started with Linear Algebra. Feel free to see this article as a buffet of options, of which you can pick what suits you best depending on your goal. If you like Brilliant, this link will give you a 20 percent discount for a premium subscription.