On Minor Prime Factorizations for Multivariate Polynomial Matrices

Multivariate polynomial matrix factorizations have been widely investigated during the past years due to the fundamental importance in the areas of multidimensional systems and signal processing. In this paper, minor prime factorizations for multivariate polynomial matrices are studied. We give a necessary and sufficient condition for the existence of a minor left prime factorization for a multivariate polynomial matrix. This result is a generalization of a theorem in Wang and Kwong (Math Control Signals Syst 17(4):297–311, 2005). On the basis of this result and a method in Fabiańska and Quadrat (Radon Ser Comp Appl Math 3:23–106, 2007), we give an algorithm to decide if a multivariate polynomial matrix has minor left prime factorizations and compute one if they exist.