I believe these are notes that you are referring to

https://terrytao.files.wordpress.com/2016/12/linear-algebra-...

These notes are excellent. One good thing is how often Terence Tao gives real life examples and analogies, contrary to what one may expect from a fields medal winner. From utilitarian perspective, reading Axler's book looks like comically bad use of one's time.

Thanks!

Tao's notes seem to be based on the book Linear Algebra by Friedberg, Insel and Spence. I found it to be one of the best books on Linear Algebra, better than even Hoffman/Kunze. The proofs are extremely clear, it has examples like PageRank, Markov Chains, PCA and the solutions to just about every exercise is available on Quizlet.

Because the poor guy contributes so much to math and math exposition and yet has his name misspelled everywhere, I'll mention that it's Terence, not Terrance.

The Tao that can be spelled is not the true Tao.

I'm not sure that Axler's book is great as a first LA book. I would go with something more traditional like Strang.

Although I really didn't feel like I "got" LA until I learned algebra (via Artin). By itself LA feels very "cookbook-y", like just a random set of unrelated things. Whereas in the context of algebra it really makes a lot more sense.

>I'm not sure that Axler's book is great as a first LA book.

Linear Algebra Done Right is a text for beginners who want to study linear algebra in a proof based, mathematically rigorous way.

So, if you want that I think it's a good fit as a first linear algebra book.

From "Preface to Students":

> You are probably about to begin your second exposure to linear algebra. Unlike your first brush with the subject, which probably emphasized Euclidean spaces and matrices, this encounter will focus on abstract vector spaces and linear maps. These terms will be defined later, so don’t worry if you do not know what they mean. This book starts from the beginning of the subject, assuming no knowledge of linear algebra. The key point is that you are about to immerse yourself in serious mathematics, with an emphasis on attaining a deep understanding of the definitions, theorems, and proofs.

It is definitely a hard text if you haven't had exposure to linear algebra before.

The thing is, by the time you get to this book, most students have probably taken DiffEq or multivariable calculus, and had exposure to linear algebra there. (If not in high school.)

That was my path and that first introduction was awful. Axler made everything finally make sense to me.

Have you seen Macdonald's "Linear and Geometric Algebra"? I found it a much nicer introduction to the subject.

My weekly chance to gripe: unfortunately nobody who writes about GA seems to be bothered by the fact that the geometric product is basically meaningless (outside of a couple of specific examples, complex numbers and quaternions).

If they would just write only about the wedge product and omit the geometric product entirely, it would actually be a great book.

Those two are pretty big as far as specific examples go, definitely worth writing about

There are other models of the two that don't require the geometric product at all. The rest of linear algebra doesn't need it, and recasting all of it in terms of a frankly terrible operation is not helpful for intuition.

talking about amazon, someone suggested me to get gareth williams linear algebra with applications (5 bucks on ebay)

it's a good applied primer, not big on concepts, more about the mechanics, and it unlocked a lot of things in my head because dry textbook morphisms definitions sent me against imaginary walls faster than c

Terry’s book is good, but it’s tedious and wordy. It takes a lot of pages to get anywhere interesting.

Wordy books are great for self study.