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New Results on the Unimodular Equivalence of Multivariate Polynomial Matrices

Author

Listed:
  • Dongmei Li

    (School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China)

  • Zuo Chen

    (School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China)

Abstract

The equivalence of systems is a crucial concept in multidimensional systems. The Smith normal forms of multivariate polynomial matrices play important roles in the theory of polynomial matrices. In this paper, we mainly study the unimodular equivalence of some special kinds of multivariate polynomial matrices and obtain some tractable criteria under which such matrices are unimodular equivalent to their Smith normal forms. We propose an algorithm for reducing such n D polynomial matrices to their Smith normal forms and present an example to illustrate the availability of the algorithm. Furthermore, we extend the results to the non-square case.

Suggested Citation

  • Dongmei Li & Zuo Chen, 2023. "New Results on the Unimodular Equivalence of Multivariate Polynomial Matrices," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2745-:d:1173208
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