On minor prime factorizations for multivariate polynomial matrices
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Multivariate polynomial matrix factorizations have been widely investigated during the past years due to the fundamental importance in the areas of multidimensional systems and signal processing. In this paper, minor prime factorizations for multivariate polynomial matrices are studied. We give a necessary and sufficient condition for the existence of a minor left prime factorization for a multivariate polynomial matrix. This result is a generalization of a theorem in Wang and Kwong (Math Control Signals Syst 17(4):297–311, 2005). On the basis of this result and a method in Fabiańska and Quadrat (Radon Ser Comp Appl Math 3:23–106, 2007), we give an algorithm to decide if a multivariate polynomial matrix has minor left prime factorizations and compute one if they exist.
KeywordsMultidimensional systems Multivariate polynomial matrices Matrix factorizations Minor prime factorizations
The authors would like to thank the reviewers whose valuable and constructive comments helped to improve this paper.
- Bose, N. K., Buchberger, B., & Guiver, J. P. (2003). Applied multidimensional systems theory. Dordrecht: Kluwer.Google Scholar
- Decker, W., Greuel, G. M., Pfister, G., & Schönemann, H. (2015). Singular 4-0-2—A computer algebra system for polynomial computations. http://www.singular.uni-kl.de. Accessed 20 Dec 2016.
- Matsumura, H., & Reid, M. (1989). Commutative ring theory. Cambridge: Cambridge University Press.Google Scholar
- Pommaret, J. F. (2001). Solving Bose conjecture on linear multidimensional systems. In Proceedings of the European control conference (pp. 1853–1855).Google Scholar