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

vector spaceAn 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)