Any time you're dealing with linear transformations of vectors (ie functions f such that f(u + v) = f(u) + f(v) and f(a * u) = a * f(u) for any vectors u,v and

Any time you're dealing with linear transformations of vectors (ie functions f such that f(u + v) = f(u) + f(v) and f(a * u) = a * f(u) for any vectors u,v and scalar a), then you're implicitly dealing with matrices.