I’m not sure how else you’d describe a vector than something that lives in a vector space. The approach of a mathematician might be different but I do believe t

I’m not sure how else you’d describe a vector than something that lives in a vector space. The approach of a mathematician might be different but I do believe the idea of scaling and adding things (and then stuff like inner products) is a lot more important than axioms. And at least to me the rules for manipulating them fall out after a huge amount of technical work and details.