A transformation T: V->W (from a vector space V to a vector space W) is linear iff:
For all X,Y belonging to W and scalar c
T(X+Y) = T(X) +T(Y)
T(cX) = cT(X)
That is, a
transformation from a
vector space V to a
vector space W is linear iff W is both
closed under addition and
closed under scalar multiplication.