As a math educator, I strongly dislike both Strang and Axler for a 1st course. I've heard great things about Strang's lectures, but his book is disorganized and too heavy on computation. Axler's book is wonderful, but as explicitly stated on the back cover, it's designed for a 2nd course and primarily aimed at math majors.

I recommend and teach my YouTube Live series out of Fraleigh [1], but unfortunately it's out of print. Lay seems to be a good modern alternative.

[1] https://linear.mathcanbeahobby.com

I found Linear Algebra by Friedberg, Insel and Spence to be excellent. Very clear, modern notation, great exercises. It's also what Tao lectured from in 115A: https://www.math.ucla.edu/~tao/resource/general/115a.3.02f/

I've taught out of the first three of these. If I had to pick one for a first study, I'd vote for Strang -- and watch his videos while you go. Our second-semester mostly-math-majors linear algebra course uses Axler, which I think is nice for the purpose, but our students already have done a semester of computational stuff first. (Though the complete absence of any computations in the book means they don't always connect the material from the two courses very well.)

LADW saved me in undergrad, but I was pretty much exactly the target audience in an honors-level freshman math course:

"[per Treil, LADW is for] a student who, while not yet very familiar with abstract reasoning, is willing to study more rigorous mathematics than what is presented in a “cookbook style” calculus type course."

But yeah it's really attempting to introduce you to higher mathematics rather than get you comfortable doing linear algebra per se.

Strang is simpler and clearer. Axler is more advanced in the sense that it doesn’t tie it to matrices. Strange is a “first course” book, Axler is a second course.

Strang's lecture series are a nice and friendly accompaniment, especially if you don't have a reading group https://www.youtube.com/watch?v=7UJ4CFRGd-U&list=PL221E2BBF1...

LADW and LADR are great too, for an honors approach with more focus on proofs. To me it would make more sense on a second pass.

I really recommend Matrix Analysis and Applied Linear Algebra by Carl Meyer. It's both concise and comprehensive. Strange is very good, but feels kinda vague and long winded in comparison (very good for a high level understanding of the tools you're dealing with)

If you liked 3B1B and prefer intuition/applications-heavy view, then definitely Strang over Axler. Check out especially his newer textbook "Linear Algebra and Learning from Data".

Axler is more of a pure math textbook - if you want to dive more into proofs and abstractions.

You zoomers are making a list of linear algebra books and not citing Lang? Get off my lawn ;)

I strong second Strang. His book is the best first introduction to linear algebra, with "Done Right" marketing itself as a second course. Axler is notoriously shy with matrices, but Axler introduces them up front and uses them for the rest of the book.

+1 for Strang.

Lorenzo Sadun's Linear Algebra: The Decoupling Principle would probably be enough too if you added something about determinants.

The nature of textbooks is that each one is better suited for a certain profile of reader. It depends a lot on the way the reader has learnt to learn things until that point in their life.

If you liked 3B1B's style, you will prefer strang over axler. Axler and treil to a greater extent focus on bringing out the abstract elegance and the kind of rigour a math major enjoys. Strang's book also has videos accompanying - on MIT OCW.

B&V VMLS on your list is interesting - they focus a lot on real-world instantiations of the concepts and have you code up things in the (excellent) exercises. Depending on your goals, you can do only this, or strang and then this. Definitely look at the exercises in any case though.

+1 for Boyd