Agreed. I think that the distinction between the objects and their possible representations should be made clear from the beginning, simply because it will make

Agreed. I think that the distinction between the objects and their possible representations should be made clear from the beginning, simply because it will make things easier to understand. IMO, just a couple of chapters from an introductory pure mathematics book is actually the most "to the point" place to start even for people who are not huge fans of math. Just the precise definition of a vector space over a field, a linear operator, a vector basis, the derivation of matrix elements, the usual related examples and some "gymnastics" on paper can make stuff "click" and be a great start for any intended application.