The Free On-line Dictionary of Computing (30 December 2018):

vector space

    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)