nLab basis of a vector space




For kk a field and VV a free 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.


In representation theory:

Specifically in representation theory of the symmetric group:

Last revised on March 7, 2023 at 16:20:21. See the history of this page for a list of all contributions to it.