I am taking a course in machine learning and have found that the linear algebra and multivariable calculus from my engineering degree only take me part way in understanding some derivations.
One specific example is differentiating things related to matrices (like differentiating wrt a matrix whose determinant appears in the function...) But this is by no means the only fuzzy bit. I have done just enough geometry, linear algebra and low dimensional calculus to have a notion that these things somehow extend into things involving matrices and things involving high dimensional spaces.
I've tried looking on places like wikipedia's topic listing in mathematics, the page "Categories within Mathematics" at arxiv.org, and undergraduate mathematics curricula however I don't think I even know enough to know whether I'm looking at what I'm looking for... if that makes sense....
Also, I've found some compilations of matrix derivatives but a) it's disconnected from any context and b) seems like a cookbook solution and so these haven't been satisfying.
So... how does what I'm saying here map to topics in mathematics?
If I can cheat and ask a "sub question"... whatever these topics end up being, what are some typical paths people take to get from fairly applied linear algebra and calculus to these "advanced" topics? Items on such a path could be books, names of courses, whatever... I just need some guidance towards context and prerequisites.