Well, I am sure the meat of the theorem is just in those eigenvalues of the minors. Which are not even defined in the statement of the theorem. That's not academic. That's just bad style.
Part of the art of mathematical exposition is to walk the line between under and over explaining your process based on your audience.
If the intended audience is academic mathematicians or even just people with a math degree, then the notation is probably familiar. I imagine that's the target audience here.