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 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.

The polynomial x2 + y2 is irreducible over R[x,y], but can be written as
 * Example:


 * $$\left[\begin{array}{cc}

x & -y \\ y & x \end{array}\right]\left[\begin{array}{cc} x & y \\ -y & x \end{array}\right] = (x^2 + y^2) \left[\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right]$$