S> (Or "linear tranSformation") A function from a vector Space to a vector Space which reSpectS the additive and multiplicativeStructureS 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)