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.

Last revised on March 9, 2017 at 03:19:38. See the history of this page for a list of all contributions to it.