Yes, it is written for people who deal with minor matricies all the time. Academic papers are incremental materializations -- it is up to the reader to bring or build the requisite base understanding.
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.