A FORMAL THEORY OF MATRIX PRIMENESS

Primeness of no polynomial matrices is of fundamental importance in mu ltidimensional systems theory. In this paper we define a quantity whic h describes the ''amount of primeness'' of a matrix and identify it as the concept of grade in commutative algebra. This enables us to produ ce a theory which unifies many existing results, such as the Bezout id entities and complementation laws, while placing them on a firm algebr aic footing. We also present applications to autonomous systems, behav ioural minimality of regular systems, and transfer matrix factorizatio n.