The primeness degree of an nD polynomial matrix
The primeness degree of an nD polynomial matrix
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.
4254-9
Wood, J.
65587872-7126-469a-851a-d60195d39058
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72
Owens, D.H.
db24b8ef-282b-47c0-9cd2-75e91d312ad7
1997
Wood, J.
65587872-7126-469a-851a-d60195d39058
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72
Owens, D.H.
db24b8ef-282b-47c0-9cd2-75e91d312ad7
Wood, J., Rogers, E. and Owens, D.H.
(1997)
The primeness degree of an nD polynomial matrix.
36th IEEE Conference on Decision and Control, , San Diego, United States.
12 Dec 1997.
.
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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 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: 1997
Venue - Dates:
36th IEEE Conference on Decision and Control, , San Diego, United States, 1997-12-12 - 1997-12-12
Organisations:
Southampton Wireless Group
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Local EPrints ID: 250464
URI: http://eprints.soton.ac.uk/id/eprint/250464
PURE UUID: 2a3fb86c-f15e-4a4b-be80-01d9c422a817
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Date deposited: 13 Feb 2000
Last modified: 05 Mar 2024 02:33
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Contributors
Author:
J. Wood
Author:
E. Rogers
Author:
D.H. Owens
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