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On minor prime factorizations for multivariate polynomial matrices

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Abstract

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.

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Acknowledgements

The authors would like to thank the reviewers whose valuable and constructive comments helped to improve this paper.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry Of Education of China), Hunan Normal University, Changsha, 410081, Hunan, China

    Jiancheng Guan, Weiqing Li & Baiyu Ouyang

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  1. Jiancheng Guan
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  2. Weiqing Li
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  3. Baiyu Ouyang
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Corresponding author

Correspondence to Jiancheng Guan.

Additional information

This work was supported by the National Science Foundation of China under Grant 11371131.

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Guan, J., Li, W. & Ouyang, B. On minor prime factorizations for multivariate polynomial matrices. Multidim Syst Sign Process 30, 493–502 (2019). https://doi.org/10.1007/s11045-018-0566-4

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  • DOI: https://doi.org/10.1007/s11045-018-0566-4

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