Multidimensional Linear Functions

A function f: Reals^N ® Reals^M is linear if it has the form

f(x) = Ax

for some M ´ N matrix A.

Still more interestingly, f: Reals^N ´ Reals^M ® Reals^K is linear if it has the form

f(s, x) = Cs + Dx

for some K ´ N matrix C and K ´ M matrix D.