vector space

A vector space, also known as a linear space, is the most fundamental concept in linear algebra. A vector space is a set of vectors together with a field of scalars such that: the sum of any two members of the set is a vector also in the set, and multiplication of a member of the set by a member of the field produces a vector also in the set. It is a generalization of the set of all geometrical vectors and is used throughout modern mathematics. Like the concepts of a group, a ring, and a field, that of a vector space is entirely abstract.