This pairs really well with the little book https://github.com/little-book-of/linear-algebra, I have recently updated it with more content and clearer explanations, so if you're diving into this topic, you might find it helpful.
If a person has the goal of getting into a field like computer vision or machine learning, would they be able to build useful things right away if they completed this book?
I think it is actually delusional to say that a book which does not properly define what a vector is, contains the "core ideas" of linear algebra.
Linear algebra is so much more than lines in R^n. It is a powerful theory because it is abstract.
No, you aren't. How would you explain that matrices are both linear transformations and vectors? How would explain what a dual space is? How would you understand the properties of the Fourier transformation, which is a mapping between functions, which are also vectors, and itself also is a vector?
i’m as much with bourbaki as the next guy. but that’s not really how most engineers learn in practice.
as for treating linear maps between finite dimensional spaces as vectors that’s quite straightforward to do in coordinate terms.
again i refer you to the classics like Golub and van Lean that have been reprinted many many times and educated generations.
Seems like a valid definition of a vector to me. What should be added or removed, in your view?