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Degrees of greatest common divisors of invariant factors of two regular polynomial matrices

Published online by Cambridge University Press:  24 October 2008

S. Barnett
S. Barnett
Affiliation:
Department of Mathematics, University of Technology, Loughborough, Leicestershire
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Abstract

In a previous paper it was shown that a necessary and sufficient condition for two regular polynomial matrices T and U to have relatively prime determinants is that a certain matrix R be non-singular. This generalization of the resultant of two scalar polynomials is extended to give an expression for the sum of the degrees of the greatest common divisors of all pairs of invariant factors of T and U in terms of the rank of R. Further, if rank R exceeds a given value then specified pairs of factors are relatively prime.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 66 , Issue 2 , September 1969 , pp. 241 - 245
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Archbold, J. W.Algebra, p. 412 (London, 1964).Google Scholar
(2)Barnett, S.Regular polynomial matrices having relatively prime determinants. Proc. Cambridge Philos. Soc. 65 (1969), 585–590.CrossRefGoogle Scholar
(3)Rosenbrock, H. H.Some properties of relatively prime polynomial matrices, Electronics Letters 4 (1968), 374–375.Google Scholar