Down with Determinants is a paper, and I guess it is super-clear once you know the stuff already. For non mathematicians, and people who'd like to learn linear algebra? Right...

Anyway, who is missing the role of the basis? It's in practically every textbook, including the one I used.

I agree with the maths that you've written, but it's the same thing that the textbook explains, practically in the same way. The road to understanding is not the same for all people, I guess...