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In mathematics, a matrix factorization of a polynomial is an 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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  • Matrix factorization of a polynomial (en)
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  • In mathematics, a matrix factorization of a polynomial is an 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)
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  • In mathematics, a matrix factorization of a polynomial is an 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)
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