Ask HN: What's the Most Efficient Method of Learning Linear Algebra?

- MIT 18.06 - https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra... - The lectures and the textbook for the course are a default recommendation.

- Linear Algebra Done Right - This is a textbook, there are also youtube videos from the author - https://www.youtube.com/playlist?list=PLGAnmvB9m7zOBVCZBUUmS...

- Khan Academy - https://www.khanacademy.org/math/linear-algebra - Also a good place to start, very accessible, missing some of the more advanced material.

- 3blue1brown - https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x... - These videos are good but they're more of a nice overview than a way to learn.

Every undergrad level math subject (real analysis, linear algebra, topology etc) has a few core theorems around which everything revolves. Unfortunately, math textbook writers bow to the tradtition of writing bloated books where the core ideas get lost in the sea of chaff. The exercises sections usually further muddy the waters with ridiculous number of irrelevant garbage. This makes learning math not only inefficient, but also ineffective. Thus, in the present there's probbly no such book or method.

However, you can make learning LA massively more enjoyable if you choose the right books (read "books with tons of examples" that clarify theorems, definitions and the like). For example, Linear Algebra: Step by Step by Kuldeep Singh [0]is an awesome book.

[0] https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/...

It depends on your desired emphasis -- theoretical or computational?

From a more theoretical angle, Jim Hefferon has written an outstanding introductory book. It is free and open source, available with loads of supplementary material, here:

https://hefferon.net/source.html

From a computational perspective, I've heard good things about Gilbert Strang's book, although I haven't read it personally. User superbcarrot linked to his MIT course materials, including video lectures.

One word of caution though: as a mathematics educator, I don't endorse "efficiency" as a goal. When I have pursued this goal myself, I have generally regretted it, and decided in retrospect that I was largely wasting my time.

To really learn math you should: do a ton of exercises, come up with your own questions and try to answer them, be willing to explore blind alleys.

Good luck!

Terrence Tao's notes are a great resource:

https://www.math.ucla.edu/~tao/resource/general/115a.3.02f/w...

Unlike most texts I've seen, he focuses on the algebraic properties of linear objects first. Others seem to prefer to start with the algorithms of matrix operations. Of course you need to understand both so it's a matter of style/preference etc.

Also take a look at Shilov's Linear Algebra. Two things it has going for it is that it's a lot cheaper and more compact than most books. On the other hand, it's dense, and doesn't really lean on geometry to explain anything. The 3blue1brown videos make a great compliment to it (or to any book).

Immersive Linear Algebra: http://immersivemath.com/ila/index.html

Hand computation mixed with theory.