But to do that, I'll need to introduce a new notation for matrix derivatives, and it turns out that, sort of, the notation I'm about to define here just in my own personal work has turned out to be one of the most useful things that I actually use all the time, to have a notation of how to take derivatives with respect to [matrixes|matrices], so that you can solve for the minimum of J of theta with, like, a few lines of algebra rather than writing out pages and pages of matrices and derivatives. 