Monomial basis Guide, Meaning , Facts, Information and Description

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.

Table of contents

1 Definition 2 Notes 3 Examples 4 See also

Definition

The monomial basis for the vector space 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

Notes

A polynomial can always converted into monomial form by calculating Taylor expansion around 0.

Examples

A polynomial in

See also

• Polynomial sequence
• Newton polynomial
• Lagrange polynomial
• Bernstein form
• Chebyshev form

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