# Theory of probability – Kolmogorov forward for multivariable SDE

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?