VECTOR SPACE

[vector space] n (1937): a set representing a generalization of a system of vectors and consisting of elements which comprise a commutative group under addition, each of which is left unchanged under multiplication by the multiplicative identity of a field, and for which multiplication by the multiplicative operation of the field is commutative, closed, distributive such that both c(A plus B) cA plus cB and (c plus d)A cA plus dA, and associative such that (cd)A c(dA) where A, B are vectors and c, d are elements of the field