Matrix factorization of a polynomial

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 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

References

External links

• A Mathematica implementation of an algorithm to matrix-factorize polynomials