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Factorization for n-D Polynomial Matrices over Arbitrary Coefficient Field

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Abstract

Multivariate (n-D) polynomial matrix factorization is one of important research contents in multidimensional (n-D) systems, circuits, and signal processing. In this paper, several results on n-D polynomial matrices factorization over arbitrary coefficient fields are proved. Based on these results, generalizations of some results on general matrix factorization are obtained for given n-D polynomial matrices whose maximal order minors or lower order minors satisfy certain conditions. The proposed results fit for arbitrary coefficient field and have a wide range of application.

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Acknowledgements

The authors are grateful to the anonymous referees for their instructive and helpful comments, which have significantly improved the presentation of this paper.

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Authors and Affiliations

  1. School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan, 411201, China

    Jinwang Liu, Dongmei Li & Licui Zheng

Authors
  1. Jinwang Liu
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  2. Dongmei Li
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  3. Licui Zheng
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Corresponding author

Correspondence to Dongmei Li.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11871207 and 11471108, the Natural Science Foundation of Hunan provincial under Grant No. 2017JJ3084, and the Scientific Research Fund of Education Department of Hunan Province under Grant No. 17C0635.

This paper was recommended for publication by Editor LI Hongbo.

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Liu, J., Li, D. & Zheng, L. Factorization for n-D Polynomial Matrices over Arbitrary Coefficient Field. J Syst Sci Complex 33, 215–229 (2020). https://doi.org/10.1007/s11424-019-8016-4

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  • DOI: https://doi.org/10.1007/s11424-019-8016-4

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