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 representation theory, Lusztig's canonical basis and closely related Kashiwara's crystal basis in quantum groups and their representations
Famous quotes containing the words canonical and/or basis:
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—Thomas Hobbes (1579–1688)
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—Mark Twain [Samuel Langhorne Clemens] (1835–1910)