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I'm curious what you think of the "No Bullshit Guide to Linear Algebra" [1]? I'm considering buying it to refresh my knowledge from school. Or what books do you suggest?

[1] https://www.amazon.com/No-bullshit-guide-linear-algebra/dp/0...

It... more or less passes the test?

I mean, it defines matrix-vector product in a nice but abstract way, and then in the next paragraph explains why we chose that definition. And it does say "this, this here is the one important idea in this book", which it gets many points for.

I really would prefer a textbook to start with "ok, here's something we want to do. Lets figure out a formula for it. Now lets give it the name matrix-vector product".

Same for matrix-matrix products.

I don't know any really good linear algebra books, in my school it was taught the worst possible way (define a field, rote-learn the mechanical operation of matrix multiplication, talk about vector spaces for a while, talk about matrices, first mention linear transformations). Some people on this thread gave other suggestions, I'd start reading a few and choose the one I connect with the best.

Anyway, I really learned linear algebra from using it.

Here is a direct link to the page in the preview of the book where the matrix-product-is-the-same-as-linear-transformation idea first appears: https://minireference.com/static/excerpts/noBSguide2LA_previ...

I can't quite tell if the book passes the test, since the entry-point is the definition of matrix-vector product which is very close to a "complicated formula with a couple of nested sigmas" but the book also mentions the notion of matrix representations, so hard to tell overall.

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