thank you for your remarks. A few times I thought quantum mechanics from scratch (http://migdal.wikidot.com/en:quantum-outlines), but you are right that even braket notation needs some time, before one understands it and get used to it. And if 'decypher my mathematical notation' is a puzzle, then it is not the most enjoyable kind of puzzle.
Braket - I will delete it (or elaborate carefully).
For other stuff - my goal is explain off-diagonal elements in density matrix. Within this constraint, I want to make it as accessible as possible. Some matrix calculus is necessary. Popular-science level of quantum mechanics as well. It _might_ be useful to be after some introduction to quantum mechanics, but I think it is not a requirement.
In any case, I will change some stuff and test it on some smart friends, who are not physicists.