Editing Canonical basis (section)

{{Short description|Basis of a type of algebraic structure}}
In [[mathematics]], a '''canonical basis''' is a basis of an [[algebraic structure]] that is canonical in a sense that depends on the precise context:

* In a [[coordinate space]], and more generally in a [[free module]], it refers to the [[standard basis]] defined by the [[Kronecker delta]].
* In a polynomial ring, it refers to its standard basis given by the [[monomial]]s, <math>(X^i)_i</math>.
* For finite extension fields, it means the [[polynomial basis]].
* In [[linear algebra]], it refers to a set of ''n'' linearly independent [[generalized eigenvector]]s of an ''n''×''n'' matrix <math>A</math>, if the set is composed entirely of [[Jordan chain]]s.<ref>{{harvtxt|Bronson|1970|p=196}}</ref>
* In [[representation theory]], it refers to the basis of the [[quantum groups]] introduced by Lusztig.