Monomial basis
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In mathematics a monomial basis is a way to uniquely describe a polynomial using a linear combination of monomials. This description, the monomial form of a polynomial, is often used because of the simple structure of the monomial basis.
Polynomials in monomial form can be evaluated efficiently using the Horner algorithm.
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[edit] Definition
The monomial basis for the vector space Πn of polynomials with degree n is the polynomial sequence of monomials
The monomial form of a polynomial 
is a linear combination of monomials
alternatively the shorter sigma notation can be used
[edit] Notes
A polynomial can always be converted into monomial form by calculating its Taylor expansion around 0.
[edit] Examples
A polynomial in Π4
- 1 + x + 3x4
