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A formal theory of matrix primeness

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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 Bézout 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.

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This work has been sponsored by EPSRC Grant No. GR/K 18504.

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Wood, J., Rogers, E. & Owens, D.H. A formal theory of matrix primeness. Math. Control Signal Systems 11, 40–78 (1998). https://doi.org/10.1007/BF02741885

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  • DOI: https://doi.org/10.1007/BF02741885

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