Coprime factorizations of multivariate rational matrices (Q1577556)

Coprime factorizations of rational matrices of one variable are extensively used in one-dimensional systems theory. When passing to more than one independent variables, several nonequivalent generalizations of the coprimeness notion appear. In the paper under review, the generalized version of factor coprimeness for polynomial matrices in several variables is considered. In this setting, two polynomial matrices \(D, N\) are left coprime iff the block matrix \([\begin{matrix} N -D\end{matrix} ]\) is a minimal left annihilator. The author describes an algorithm for obtaining a left coprime factorization of a given rational matrix. Certain properties of coprime factorizations are established.