nLab
basis of a vector space

Contents

Definition

For kk a field and VV a kk-vector space, a basis for VV is a basis of a free module for VV regarded as a free module over kk. 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.

Revised on October 28, 2013 21:35:44 by Urs Schreiber (82.169.114.243)