A formal theory of matrix primeness

Description/Abstract

Primeness of nD polynomial matrices is of fundamental importance in multidimensional systems theory. In this paper we define a quantity which describes the ``amount of primeness'' of a matrix and identify it as the concept of grade in commutative algebra. This enables us to produce a theory which unifies many existing results, such as the Bezout identities and complementation laws, while placing them on a firm algebraic footing. We also present applications to autonomous systems, behavioural minimality of regular systems, and transfer matrix factorization.