About: Matrix factorization of a polynomial

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In mathematics, a matrix factorization of a polynomial is a technique for factoring irreducible polynomials with matrices. David Eisenbud proved that every multivariate real-valued polynomial p without linear terms can be written as a AB = pI, where A and B are square matrices and I is the identity matrix. Given the polynomial p, the matrices A and B can be found by elementary methods. * Example: The polynomial x2 + y2 is irreducible over R[x,y], but can be written as

Property	Value
dbo:abstract	In mathematics, a matrix factorization of a polynomial is a technique for factoring irreducible polynomials with matrices. David Eisenbud proved that every multivariate real-valued polynomial p without linear terms can be written as a AB = pI, where A and B are square matrices and I is the identity matrix. Given the polynomial p, the matrices A and B can be found by elementary methods. * Example: The polynomial x2 + y2 is irreducible over R[x,y], but can be written as (en)
dbo:wikiPageExternalLink	https://mathematica.stackexchange.com/a/222542
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dbo:wikiPageWikiLink	dbr:David_Eisenbud dbr:Matrix_(mathematics) dbc:Polynomials_factorization_algorithms dbr:Identity_matrix dbr:Irreducible_polynomial dbc:Algebra dbc:Polynomials dbr:Square_matrices dbr:Multivariate_polynomial
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dcterms:subject	dbc:Polynomials_factorization_algorithms dbc:Algebra dbc:Polynomials
rdfs:comment	In mathematics, a matrix factorization of a polynomial is a technique for factoring irreducible polynomials with matrices. David Eisenbud proved that every multivariate real-valued polynomial p without linear terms can be written as a AB = pI, where A and B are square matrices and I is the identity matrix. Given the polynomial p, the matrices A and B can be found by elementary methods. * Example: The polynomial x2 + y2 is irreducible over R[x,y], but can be written as (en)
rdfs:label	Matrix factorization of a polynomial (en)
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