About: Polarization of an algebraic form

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In mathematics, in particular in algebra, polarization is a technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables. Specifically, given a homogeneous polynomial, polarization produces a unique symmetric multilinear form from which the original polynomial can be recovered by evaluating along a certain diagonal.

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rdf:type	topical concept yago:Abstraction100002137 yago:Function113783816 yago:HomogeneousPolynomial105862268 yago:MathematicalRelation113783581 yago:Polynomial105861855 yago:Relation100031921 yago:WikicatHomogeneousPolynomials
rdfs:label	극성화와 반환 (ko) Polarization of an algebraic form (en)
rdfs:comment	가환대수학에서 극성화(極性化, 영어: polarization)는 동차 다항식에 변수를 추가하여 다중 선형 다항식으로 변환시키는 연산이다. 반환(返還, 영어: restitution)은 극성화의 반대 연산이며, 다중 선형 다항식을 동차 다항식으로 변환시킨다. (ko) In mathematics, in particular in algebra, polarization is a technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables. Specifically, given a homogeneous polynomial, polarization produces a unique symmetric multilinear form from which the original polynomial can be recovered by evaluating along a certain diagonal. (en)
dct:subject	Abstract algebra Homogeneous polynomials
Wikipage page ID	5558285 (xsd:integer)
Wikipage revision ID	1088603955 (xsd:integer)
Link from a Wikipage to another Wikipage	Representation theory Degree of a polynomial Indeterminate (variable) Mathematics Claudio Procesi Commutative ring Topological vector space Algebra Algebraic geometry Field (mathematics) Graded ring Multilinear form Quadratic form Invariant theory Abstract algebra Symmetric algebra Symmetric power Homogeneous polynomial Homogeneous polynomials Polarization identity Polynomial ring Positive characteristic Characteristic zero dbr:Weyl's_invariant_theory
sameAs	Polarization of an algebraic form Polarization of an algebraic form Polarization of an algebraic form Polarization of an algebraic form Polarization of an algebraic form
dbp:wikiPageUsesTemplate	dbt:About dbt:Annotated_link dbt:Short_description dbt:Isbn
has abstract	In mathematics, in particular in algebra, polarization is a technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables. Specifically, given a homogeneous polynomial, polarization produces a unique symmetric multilinear form from which the original polynomial can be recovered by evaluating along a certain diagonal. Although the technique is deceptively simple, it has applications in many areas of abstract mathematics: in particular to algebraic geometry, invariant theory, and representation theory. Polarization and related techniques form the foundations for . (en) 가환대수학에서 극성화(極性化, 영어: polarization)는 동차 다항식에 변수를 추가하여 다중 선형 다항식으로 변환시키는 연산이다. 반환(返還, 영어: restitution)은 극성화의 반대 연산이며, 다중 선형 다항식을 동차 다항식으로 변환시킨다. (ko)
gold:hypernym	Technique
prov:wasDerivedFrom	wikipedia-en:Polarization_of_an_algebraic_form?oldid=1088603955&ns=0
page length (characters) of wiki page	5962 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Polarization_of_an_algebraic_form
is Link from a Wikipage to another Wikipage of	Quadratic Jordan algebra Gateaux derivative Polarization Projective variety Symmetric cone Homogeneous polynomial Polarization identity Spherical harmonics Spinors in three dimensions Polarization formula
is Wikipage redirect of	Polarization formula
is Wikipage disambiguates of	Polarization
is foaf:primaryTopic of	wikipedia-en:Polarization_of_an_algebraic_form

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