Depending on your background and intentions, you might like:

Savov: https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0...

Strang: https://www.amazon.com/Linear-Algebra-Learning-Gilbert-Stran...

Klein: https://www.amazon.com/Coding-Matrix-Algebra-Applications-Co...

I think the pacing and exercises in the above Strang book are great.

I'll second Strang. I recently re-read his Introduction to Linear Algebra and was struck with how clearly he explains things compared to most other math textbooks (which I've been reading a lot of lately).

Boyd and Vandenberghe's Introduction to Applied Linear Algebra [1].

[1] https://web.stanford.edu/~boyd/vmls

"Linear Algebra Done Right" https://linear.axler.net/

There's a compact and free form on the book on that page.

Heed Axler's warning; the compact version is meant as a refresher, not a book to learn from.

> Linear Algebra Abridged is generated from Linear Algebra Done Right (third edition) by excluding all proofs, examples, and exercises, along with most comments. Learning linear algebra without proofs, examples, and exercises is probably impossible. Thus this abridged version should not substitute for the full book. However, this abridged version may be useful to students seeking to review the statements of the main results of linear algebra.

Maybe you previously worked through the full LADR (or some other math-major linear algebra book like the older, classic Halmos), but your memory is fuzzy. That might be a use for it.

Still, I don't know why you'd read through a 150 page refresher rather than the full book. If you can't afford it, the 3rd edition is on libgen like most other textbooks.

The book is not easy. It's more like a traditional textbook, albeit a great one. In my experience, the book is great at showing how seemingly hard concepts can be systematically developed, layer by layer, under the framework of vector space and linear transformation. When reading the book, I often marveled like this: that's it? Wow! A few references to the previously listed theorems and definitions and this is proved?

Axler is not easy. (At least, I did not find it easy.)

I think that book is usually recommended as a good book to learn from after you've already been through a course in linear algebra.

Axler won't really teach you to calculate though.

Axler's approach puts the cart behind the horse where it belongs. Learning to do row reduction by hand is a really pointless exercise that misses the forest for the trees. But if want want the nitty gritty on computation, Golub and Van Loans "Matrix Computations" is pretty classic.

Only if you want to be a real mathematician. Most people don't and are better served by learning to calculate, since that teaches you how the techniques of linear algebra are applied.

You actually do need to learn to do row reduction by hand because it teaches you what is going on. Same reason you need to learn to integrate by hand even though you'll never do it again after your coursework.

BTW, I learned linear algebra from Axler first, so I have some basis for comparison. There is a reason Axler is not considered an introductory text even though it is not very hard.

The YouTube channel 3Blue1Brown has an "Essence of Linear Algebra" series that I found helpful (along with an Essence of Calculus series and videos on other tricky subjects such as differential equations and Fourier transforms). I found that the visual approach of the videos helped make the concepts more intuitive.

There's Serge Lang's Basic Mathematics which discusses algebra and geometry, including a bit of linear algebra. Introduction to Linear Algebra, by the same author is a bit deeper. Those are the textbooks I would pair with Calculus Made Easy.

For slightly less mature students, there's Algebra by Gelfand.

I really waned to like the Gefland books, and Algebra starts off so well, but they are actually intended as barebones exercise books to go along with lectures which introduce the problems. Or, they could for advanced students who are interested in revisiting the basics. As books, the experience is maddeningly incomplete, and they do not teach mathematics to the uninitiated. I wouldn’t recommend them to anyone who either wants to relearn high school math or learn from ground zero. During self study, I hit a wall about 25% through, and after checking solutions online it turned out that the problem was extremely advanced and also had an error of some kind which renders the solution impossible. I learned some behind the scenes aspects of the book such as the course and lecture which are missing, and I gave up at that point

I think Lang, though tough, actually would be a better book to learn from. It actually seems comprehensive and designed for motivated people who want a very solid understanding of math, but are actually possibly new to the subject.

I have some background in linear algebra from college but 3b1b really made it click for me [1]

[1] https://www.3blue1brown.com/topics/linear-algebra

I liked this. It’s a different approach so take a look at the free pages. Not for everyone but worth a look to see if it fits you. Bonus: the author is responsive.

https://machinelearningmastery.com/linear_algebra_for_machin...

it's mostly just a few key concepts such as the eigenvalue, eigenvector, the determinant, the inverse, and some others. Even the wiki does a good job describing it + youtube videos

Unfortunately, nobody can be told what a matrix is.

Sorry, what do you mean? Is this a joke or some other reference I didn't get?

It's a reference to a line from the movie The Matrix: "Unfortunately no one can be told what the Matrix is. You have to see it for yourself."