Source : Free On-Line Dictionary of Computing

linear map
     
         (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)