# Definition:Basis of Vector Space

 It has been suggested that this page or section be merged into Definition:Coordinate System. (Discuss)

## Definition

Let $K$ be a division ring.

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

### Definition 1

A basis of $G$ is a linearly independent subset of $G$ which is a generator for $G$.

### Definition 2

A basis is a maximal linearly independent subset of $G$.

## Also known as

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

## Linguistic Note

The plural of basis is bases.

This is properly pronounced bay-seez, not bay-siz.