You are quoting the lab which is all about doing stuff in numpy. Probably if you want to critique the definitions used you should switch to the book.
That said, it doesn't lead with a notion of vector that is as general as I'd like. Readers might be later surprised to find that there are vectors which are not lists of numbers. But I only looked at the first few pages so I assume the vector space axioms show up eventually.
I find it very disrespectful towards a project with such popularity to contributors ratio.
It takes long hours to produce a working notebook, a synergy between concept descriptions and theorical explanations alongside code, comments of code and markdown for the theory here and there is an artistic coupled with engineering stunt you should try to accomplish yourself before criticizing. Perhaps you have, in which case a contribution as the other comment points out is the courteous thing to do.
That book must have taken months to author and is one of the best read on the subject I've ever come across.
Edit: removed incorrect fact about scalars.. they don't have a direction they have polarity.
My intention was to suggest that my parent shouldn't be so quick to criticize while acknowledging that they may have a point.
If the latter goal outshined the former, my apologies. I love stuff like this.
The book is even worse: "A vector, by contrast, is an ordered collection of numbers."
This is a terrible definition and makes talking about proper linear algebra proper impossible.
I tried to build intuition before going into the formal definitions.
Personally, I've always liked Bourbaki's books, but they're too formal for learning - especially in linear algebra, which I see as something meant for applications rather than pure math research.
Maybe I just oversimplified things or made them feel less "math".
here you go mate, exactly what you are looking for : https://github.com/little-book-of/linear-algebra#contributin...
Every contribution is welcome: whether it's criticism, fixing typos, or even completely rewriting a section!
Writing this book has been a real challenge for me, since all the books I enjoy reading are very formal ones :))
Anyone here into Grothendieck's SGA or EGA? (Sorry, a bit off topic!)
Readers might be later surprised to find that there are vectors which are not lists of numbers
I see this sort of thing as being similar to how physics is taught. Year 1: Atoms are indivisible. Year 2: Well, no, actually, we lied, they consist of elementary particles called electrons, protons, and neutrons. Year 3: Well, technically the protons and neutrons aren't indivisible either. ... Year 10: OK, fine, we have no idea. Your turn, help us figure this out.
Nobody starts rambling about quarks and gluons in grade school, and few practitioners will ever need to deal with them at all. Likewise, for most people looking to get their feet wet in ML, vectors are a 1D list of numbers, matrices are a 2D list of numbers, and tensors are lists of numbers with any number of dimensions. Definitions that are incomplete at best, but good enough to get started.