(OR "linear transfORmation") A function from a vectOR space to a vectOR space which respects the additive and multiplicative structures of the two: that is, fOR any two vectORs, u, v, in the source vectOR space and any scalar, k, in the field over which it is a vectOR space, a linear map f satisfies f(u+kv) = f(u) + kf(v). (1996-09-30)