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.
db24b8ef-282b-47c0-9cd2-75e91d312ad7
1998
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.
(1998)
A formal theory of matrix primeness.
Mathematics of Control, Signals, and Systems, 11, .
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
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Local EPrints ID: 250452
URI: http://eprints.soton.ac.uk/id/eprint/250452
PURE UUID: 875433fe-7bc9-4278-8494-6211cd10225e
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Date deposited: 01 Jun 1999
Last modified: 18 Oct 2022 01:32
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Author:
J. Wood
Author:
E. Rogers
Author:
D.H. Owens
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