"In the following four chapters, the basic algebraic structures (groups, rings, fields, vectorspaces) are reviewed, with a major emphasis on vector spaces. Basic notions of linear algebra such as vector spaces, subspaces, linear combinations, linear independence, [...], dual spaces,hyperplanes, transpose of a linear maps, are reviewed."
If anyone needs to start even earlier than this, I've actually found "3D Math Basics for Graphics and Game Development" to be a good true intro for linear algebra-related stuff. I think this would probably hold even if your primary interest is something other than graphics/game dev. Some of the text in that book's intro is a little cringey with its reliance on kind of juvenile game references, but I didn't find that sort of writing continuing during the actual text. So just push past that stuff.
I got a copy of it to act as a refresher before diving into Real-Time Collision Detection since it's been quite a long time since formal math for me (as in, high school, because I'm self-taught in CS). I've managed to make up a lot of ground by working hard and finding classes to audit online (Strang's linear alg course on OCW is a good one), but I have found that depressingly few math texts which claim to be "introductory" are actually truly introductory.
This isn't a slight against the linked work, I absolutely love when profs make resources such as this freely available.
"How to Prove It" and "Book of Proof" are also great intros to formal math, if less immediately practical.