If I have a linear map T:V -> W and the basis of V is B={v1,...,vn} and the basis of W is B={w1,...,wm}

Then what is the formula for the matrix M_AB(T)?

It may not make much sense, but in the previous section of my notes, the formula for changing coordinates when changing bases was x=C_ABy

where x is the coordinates/vectore in the B basis, y is the coordinates/vector in the A basis and C_AB is a matrix.