(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)