# 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.