vector space <mathematics> An {additive group} on which some ({scalar}) field has an associative multiplicative action which distributes over the addition of the vector space and respects the addition of the (scalar) field: for vectors u, v and scalars h, k; h(u_v) = hu _ hv; (h_k)u = hu _ ku; (hk)u = h(ku). [Simple example?] (1996-09-30)