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Statements

Subject Item
dbr:Matrix_factorization_of_a_polynomial
rdfs:label
Matrix factorization of a polynomial
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
dcterms:subject
dbc:Polynomials dbc:Algebra dbc:Polynomials_factorization_algorithms
dbo:wikiPageID
64466245
dbo:wikiPageRevisionID
1117460933
dbo:wikiPageWikiLink
dbc:Polynomials dbc:Polynomials_factorization_algorithms dbr:David_Eisenbud dbr:Matrix_(mathematics) dbc:Algebra dbr:Square_matrices dbr:Irreducible_polynomial dbr:Multivariate_polynomial dbr:Identity_matrix
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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
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wikipedia-en:Matrix_factorization_of_a_polynomial?oldid=1117460933&ns=0
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1752
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wikipedia-en:Matrix_factorization_of_a_polynomial
Subject Item
dbr:Matrix_decomposition
owl:differentFrom
dbr:Matrix_factorization_of_a_polynomial
Subject Item
dbr:Polynomial_matrix_spectral_factorization
dbo:wikiPageWikiLink
dbr:Matrix_factorization_of_a_polynomial
Subject Item
wikipedia-en:Matrix_factorization_of_a_polynomial
foaf:primaryTopic
dbr:Matrix_factorization_of_a_polynomial