Canonical basis

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 monomials, . For finite extension fields, it means the polynomial basis. In linear algebra, it refers to a set of n linearly independent generalized eigenvectors of an n×n matrix , if the set is composed entirely of Jordan chains. In representation theory, it refers to the basis of the quantum groups introduced by Lusztig.

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