get the empirical covariance on the samples if you actually want to work through this and get this result here are some key matrix identities that are useful otherwise you probably won't get to this result and so these are just kind of things that you at some point might have derived in a previous class or might have never drived it might be a surprise right now but these are true quantities that can come in very handy when doing these multi well multidimensional derivations with gaussians you'll see these tricks will