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New Results on the Equivalence of Bivariate Polynomial Matrices

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Abstract

This paper investigates the equivalence problem of bivariate polynomial matrices. A necessary and sufficient condition for the equivalence of a square matrix with the determinant being some power of a univariate irreducible polynomial and its Smith form is proposed. Meanwhile, the authors present an algorithm that reduces this class of bivariate polynomial matrices to their Smith forms, and an example is given to illustrate the effectiveness of the algorithm. In addition, the authors generalize the main result to the non-square case.

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Author information

Authors and Affiliations

  1. KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Xiaopeng Zheng & Dingkang Wang

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Xiaopeng Zheng & Dingkang Wang

  3. School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China

    Dong Lu

  4. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, China

    Fanghui Xiao

Authors
  1. Xiaopeng Zheng
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  2. Dong Lu
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  3. Dingkang Wang
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  4. Fanghui Xiao
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Corresponding author

Correspondence to Dong Lu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 12171469, 12001030 and 12201210, the National Key Research and Development Program under Grant No. 2020YFA0712300, and the Fundamental Research Funds for the Central Universities under Grant No. 2682022CX048.

This paper was recommended for publication by Editor MOU Chenqi.

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Zheng, X., Lu, D., Wang, D. et al. New Results on the Equivalence of Bivariate Polynomial Matrices. J Syst Sci Complex 36, 77–95 (2023). https://doi.org/10.1007/s11424-023-1304-z

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  • DOI: https://doi.org/10.1007/s11424-023-1304-z

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