First Sentence

"A vector space over the numeric field K (K = R or K = C) is a nonempty set V, whose elements are called vectors and in which two operations are defined, called addition and scalar multiplication, that enjoy the following properties: 1. addition is commutative and associative; 2. there exists an element 0 V (the zero vector or null vector) such that v + 0 = v for each v V; 3. 0 . v = 0, 1 . v = v, where 0 and 1 are respectively the zero and the unity of K; 4. for each element v V there exists its opposite, -v, in V such that v + (-v) = 0; 5. the following distributive properties hold K, v, w V, (v + w) = v + w, K, v V, (+)v = v + v; 6. the following associative property holds, K, v V, ()v = (v)."