On Rank Factorizations and Factor Prime Factorizations for Multivariate Polynomial Matrices
- 24 Downloads
In this paper, rank factorizations and factor left prime factorizations are studied. The authors prove that any polynomial matrix with full row rank has factor left prime factorizations. And for a class of polynomial matrices, the authors give an algorithm to decide whether they have rank factorizations or factor left prime factorizations and compute these factorizations if they exist.
KeywordsFactor prime factorizations multivariate polynomial matrices rank factorizations
Unable to display preview. Download preview PDF.
- Bose N K, Buchberger B, and Guiver J P, Multidimensional Systems Theory and Applications, Kluwer, Dordrecht, 2003.Google Scholar
- Pommaret J F, Soving Bose conjecture on linear multidimensional systems, Proceedings of the European Control Conference, Porto, 2001.Google Scholar
- Lu D, Ma X D, and Wang D K, A new algorithm for general factorizations of multivariate polynomial matrices, Proceedings of ISSAC, Kaiserslautern, 2017, 277–284.Google Scholar
- Matsumura H and Reid M, Commutative Ring Theory, Cambridge University Press, Cambridge, 1989.Google Scholar
- Decker W, Greuel G M, Pfister G, et al., Singular 4–0-2 — A computer algebra system for polynomial computations, http://www. singular.uni-kl.de, 2015.Google Scholar