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Monomial basis

In mathematics the monomial basis of a polynomial ring is its basis (as a vector space or free module over the field or ring of coefficients) that consists of all monomials. The monomials form a basis because every polynomial may be uniquely written as a finite linear combination of monomials (this is an immediate consequence of the definition of a…

Applications, In analysis and numerical applications & Several indeterminates

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In analysis and numerical applications

Complex planeTaylor seriesDiskRadiusAnalytic
5 related topics

Several indeterminates

IntegersHomogeneous polynomialsSubspaceDimensionBinomial coefficient
7 related topics

One indeterminate

Univariate polynomialsDegreeSigma notationTotally ordered
4 related topics

Overview

MathematicsPolynomial ringBasisVector spaceFree module
11 related topics

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One indeterminate

Several indeterminates

In analysis and numerical applications

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Monomial basis

Nodes32
Edges31
Triples7
Avg. degree1.94
Density0.0625
Components1

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Monomial basis

Top relations

has application · 4
Monomial basis → Polynomials, Taylor, The, When
related to Several indeterminates · 3
Monomial basis → As, In, Similar

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Important terminology

basis displaystyle monomial monomials polynomial form ring polynomials cdots coefficients degree subspace space field ldots case vector free module also

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SubjectPredicateObjectConfidenceSrc
Monomial basishas applicationThe0.60section
Monomial basishas applicationTaylor0.60section
Monomial basishas applicationWhen0.60section
Monomial basishas applicationPolynomials0.60section
Monomial basisrelated to Several indeterminatesIn0.60section
Monomial basisrelated to Several indeterminatesAs0.60section
Monomial basisrelated to Several indeterminatesSimilar0.60section

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