Comment by phkx

Now I’m thinking that I have missed the point of the article. I didn’t read it as an introduction to vector spaces, but rather that the introduction served as to give an intuition how functions may be viewed as vectors (going back to the article, it’s even in the section heading). I found the next parts well written and to the point, leading along the steps to show that indeed the requirements for a Hilbert space are met by L^2 (even though those requirements are only spelled out in the end). I’m not actively working with mathematics any more, but I didn’t notice any major corner cutting. It’s not text book rigorous but lays out the idea in an easy to follow way. I took something away from it - or not, depending on whether I missed some inconsistency.