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A formal theory of matrix primeness

A formal theory of matrix primeness
A formal theory of matrix primeness
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.
40-78
Wood, J.
65587872-7126-469a-851a-d60195d39058
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72
Owens, D.H.
3452e9bb-d3bd-4995-b4bb-424bbd288b09
Wood, J.
65587872-7126-469a-851a-d60195d39058
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72
Owens, D.H.
3452e9bb-d3bd-4995-b4bb-424bbd288b09

Wood, J., Rogers, E. and Owens, D.H. (1998) A formal theory of matrix primeness. Mathematics of Control, Signals, and Systems, 11, 40-78.

Record type: Article

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.

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Published date: 1998
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 250452
URI: http://eprints.soton.ac.uk/id/eprint/250452
PURE UUID: 875433fe-7bc9-4278-8494-6211cd10225e
ORCID for E. Rogers: ORCID iD orcid.org/0000-0003-0179-9398

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Date deposited: 01 Jun 1999
Last modified: 25 Mar 2020 01:24

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Contributors

Author: J. Wood
Author: E. Rogers ORCID iD
Author: D.H. Owens

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