basis of a vector space



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.


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 March 9, 2017 03:19:38 by Urs Schreiber (