If you want a proof-based approach, Linear Algebra Done Right is the typical go-to that’s also on the MIRI page. I went through maybe the first 3/4ths of it, and I thought it was pretty good, in terms of number of exercises and helping you think about manipulating vector spaces, etc. in a more abstract sense.
In general, I think that 3B1B’s videos are really good for building intuition about a concept, but trying to do exercises off of the pedagogy in his videos alone can be quite challenging, especially as he often assumes some mastery with the subject already. (EX: In the eigen-stuffs video, he doesn’t actually explain how to find the eigenvalues of a matrix.)
Thus, I think it makes more sense to stick to a traditional textbook / course for learning linear algebra and using 3B1B as supplementary stuff for when you want a visual / different way of looking at a concept.
Also, it might be worth checking in to see what you want to learn linear algebra for. I suspect there are more domain specific resources if, for example, you cared about just the useful parts of linear algebra used in machine learning (dimensionality reduction, etc.).
Previous LessWrong reviews of Linear Algebra Done Right by Nate Soares and TurnTrout (both highly detailed).
Here’s a summary passage from Nate:
This book did a far better job of introducing the main concepts of linear algebra to me than did my Discrete Mathematics course. I came away with a vastly improved intuition for why the standard tools of linear algebra actually work.
I can personally attest that Linear Algebra Done Right is a great way to un-memorize passwords and build up that intuition. If you know how to compute a determinant but you have no idea what it means, then I recommend giving this book a shot.
I imagine that Linear Algebra Done Right would also be a good introduction for someone who hasn’t done any linear algebra at all.
TurnTrout’s review has links to solutions to the exercises (he did ~100% of the exercises, and talks about them a bit, which is relevant for Raemon’s question).
But, I’ve attempted that and mostly bounced off it because it felt too much like work. It might be the answer is “if you want to actually learn this thing you have to do the actual grownup thing” but by default I’m orienting around something like “the thing that seemed fun except that I didn’t quite have enough resources to grok it, can I make it work better?” than “how do I seriously pursue learning math?”
(At least for the calculus videos I’m also skeptical about whether the “mastery is assumed” problem is especially bad, although I can imagine this being true for many of the more advanced stuff)
If you want a proof-based approach, Linear Algebra Done Right is the typical go-to that’s also on the MIRI page. I went through maybe the first 3/4ths of it, and I thought it was pretty good, in terms of number of exercises and helping you think about manipulating vector spaces, etc. in a more abstract sense.
Otherwise, I’ve heard good things about Gilbert Strang’s MIT OCW course here: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/.
In general, I think that 3B1B’s videos are really good for building intuition about a concept, but trying to do exercises off of the pedagogy in his videos alone can be quite challenging, especially as he often assumes some mastery with the subject already. (EX: In the eigen-stuffs video, he doesn’t actually explain how to find the eigenvalues of a matrix.)
Thus, I think it makes more sense to stick to a traditional textbook / course for learning linear algebra and using 3B1B as supplementary stuff for when you want a visual / different way of looking at a concept.
Also, it might be worth checking in to see what you want to learn linear algebra for. I suspect there are more domain specific resources if, for example, you cared about just the useful parts of linear algebra used in machine learning (dimensionality reduction, etc.).
Previous LessWrong reviews of Linear Algebra Done Right by Nate Soares and TurnTrout (both highly detailed).
Here’s a summary passage from Nate:
TurnTrout’s review has links to solutions to the exercises (he did ~100% of the exercises, and talks about them a bit, which is relevant for Raemon’s question).
Nod.
But, I’ve attempted that and mostly bounced off it because it felt too much like work. It might be the answer is “if you want to actually learn this thing you have to do the actual grownup thing” but by default I’m orienting around something like “the thing that seemed fun except that I didn’t quite have enough resources to grok it, can I make it work better?” than “how do I seriously pursue learning math?”
(At least for the calculus videos I’m also skeptical about whether the “mastery is assumed” problem is especially bad, although I can imagine this being true for many of the more advanced stuff)