>>12252537They're vector valued functions that are linear, meaning they satisfy the linearity conditions:
f(u+v) = f(u) + f(v)
f(?v) = ? f(v)
For example (x,y) --> (xy, 0) is not linear since it maps:
u=(1,1) to (1,0)
v=(0,1) to (0,0)
yet it maps u+v = (1,2) to (2,0)
which different from f(u) + f(v) = (1,0) + (0,0) = (1,0)
On the other hand any function of the form f(x,y) = (ax+by, cx + dy) for a,b,c,d in R will do. And actually, those are the only functions that satisfy the linear property.
