Definition:Basis of Vector Space

Definition
Let $K$ be a division ring.

Let $\struct {G, +_G, \circ}_R$ be a vector space over $K$.

Also known as
A basis of a vector space can also be referred to as a basis for a vector space.

A basis of a vector space over a subfield of $\C$ may also be known as a Hamel basis, to contrast with Schauder basis.

Also see

 * Equivalence of Definitions of Basis of Vector Space
 * Definition:Dimension of Vector Space
 * Bases of Vector Space have Equal Cardinality

Generalizations

 * Definition:Basis of Module