# nLab basis of a vector space

Contents

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Definition

For $k$ a field and $V$ a free $k$-vector space, a basis for $V$ is a basis of a free module for $V$ regarded as a free module over $k$. In functional analysis, a basis in this sense is called a Hamel basis.

## Properties

The basis theorem asserts that, with the axiom of choice, every vector space admits a basis, hence that every module over a field is a free module.

## Examples

Specifically in representation theory of the symmetric group:

Last revised on May 26, 2022 at 19:11:36. See the history of this page for a list of all contributions to it.