Can you articulate on the first one? In the last semester I tutored for a Linear algebra course which used his book and it was a nightmare. Ideas seems to be presented in reverse order and a lot of students ended up having trouble understanding basic concepts.

So strange. It was the best book I’ve read about the topic. It’s been a while, but I don’t recall anything not presented in the right order. Going from linear equations to a geometric interpretation of the rows, then to linear combination of the columns. Then Gauss-Seidel to LRU.

I liked his approach of “ideas first, rigor later”. I think after reading this book, you can easily grab a book with more formalism, if you feel lacking rigor.

I’m interested to understand where you felt the order was wrong?

A bit everywhere. One thing that really bothered me is that you have to wait until chapter 3 to introduce the notion of vector spaces. I know that it is not an easy concept to grasp, but once you manage to understand it a lot of previous things become trivial.

When I was first introduced to the idea of solving linear equations, we already had the idea of space vectors and basis, so solving a system of equations was just an application of finding the coefficients of the linear combination.

> I liked his approach of “ideas first, rigor later”. I think after reading this book, you can easily grab a book with more formalism if you feel lacking rigor.

This sentence made me think. Maybe there was a disconnect between my experience (Physics background, bottom-up approach) and the one taught in the course (Data science for Linguistic, top-down). Each time I tried to use the notion and examples I had in mind with the students I found myself hitting a wall because they had not covered the topics yet.

That sounds about right. I read the book and watched the lectures after I graduated. And it was just fun.

The thing is that the ideas stuck and I was very grateful for that.

But we can be lucky that there are so many approaches out there to pick from.

You probably already know about them, but just in case: have you watched 3b1b's videos about Linear Algebra? Those did open my mind and improved my understanding of linear algebra.

Oh yes, 3b1b is my favorite. All of them, but especially Fourier series.

I tried Strang in uni and it was about the worst linear algebra book I tried. Kostrikin on the other hand was perfect — he struck the right balance between geometric intuition and formal rigour.

I haven't used his book, just watched the Youtude videos. His teaching went slowly with simple examples. He explained them really well.

There're a lot of materials, much more than one would care. He covered many topics. I just jumped to the ones I needed to learn at the time. I had Linear Algebra background so most were just a refresher for me. As a student attending the class the first time, it might be overwhelming to learn all those material in a semester.

I think for someone more interested in the formal side of things, Strang is definitely a little weird. I bounced right off it, and to this day don't really know what the rows are supposed to be about. Axler was perfect for me. But for developing an intuition for the nitty gritty operations, I think Strang is probably pretty good.

Absolutely love the first one. His explanation of SVD had a big impact on me and my dad is now teaching it in his math class haha