< mathematics > (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)