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New Results on Equivalence of Multivariate Polynomial Matrices

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Abstract

This paper investigates equivalence of square multivariate polynomial matrices with the determinant being some power of a univariate irreducible polynomial. The authors give a necessary and sufficient condition for this equivalence. And the authors present an algorithm to reduce a class of multivariate polynomial matrices to their Smith forms.

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Authors and Affiliations

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

    Jiancheng Guan, Jinwang Liu, Licui Zheng, Tao Wu & Jie Liu

Authors
  1. Jiancheng Guan
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  2. Jinwang Liu
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  3. Licui Zheng
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  4. Tao Wu
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  5. Jie Liu
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Corresponding author

Correspondence to Jinwang Liu.

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The authors declare no conflict of interest.

Additional information

This research was supported by the Scientific Research Fund of Education Department of Hunan Province, China under Grant Nos. 20C0790 and 22A0334, the National Natural Science Foundation of China under Grant Nos. 11971161, 12201204, and 12371507, and the Natural Science Foundation of Hunan Province under Grant No. 2023JJ40275.

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Guan, J., Liu, J., Zheng, L. et al. New Results on Equivalence of Multivariate Polynomial Matrices. J Syst Sci Complex (2024). https://doi.org/10.1007/s11424-024-2288-z

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  • DOI: https://doi.org/10.1007/s11424-024-2288-z

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