When looking at a 2D sd, for example for processes $ Z_t = (X_t, Y_t) ^ T $.
$ dZ_t = f (X_t, Y_t) dt + g (X_t, Y_t) dB_t $
My textbook says that diffusion is found by calculating $ D = 1/2 cdot g (X_t, Y_t) g (X_t, Y_t) ^ T $. For this case, that would lead to a $ 4 times4 $ matrix. When later I find the term advective. $ u = f (X_t, Y_t) – nabla D $What is the meaning of taking the gradient of that matrix? Or is it not like calculating the diffusion for a multivariate system?