I only skimmed this and it might be very well written, but there's a pattern I see a lot with vectors that I think should change. All over the internet we have

I only skimmed this and it might be very well written, but there's a pattern I see a lot with vectors that I think should change. All over the internet we have these introductions to LA that start this way, with vectors as arrows or lists of numbers. At the same time, we tell people that LA is enormously important in the modern world, but I think it's hard to see why. Then, usually somewhere very late in the whole thing (often only as an appendix) we have something along the lines of "oh BTW, vectors can be anything that you can scale and add, and thus can be used to model various things like documents, quantum states, fourier series etc.". But this is literally the whole point! These abstract uses of vector spaces are what make them so important in managing information. I wish someone would write a blog or make a video starting with this stuff to motivate the whole thing. Does anyone else think there's value in something like what I'm suggesting?