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<p>The Smith form of matrices plays a significant role in the reduction of multidimensional systems and the equivalence of matrices. In this paper, the authors investigate the equivalence problem for two classes of multivariate polynomial matrices and their Smith forms. The authors derive some criteria on reducing these matrices to their Smith forms. Additionally, the authors provide an example to illustrate the main results.</p>

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On the Equivalence of Two Classes of Multivariate Polynomial Matrices and Smith Forms

  • 期刊论文

  • 发表日期：

    2026年4月7日

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  • Zuo Chen,
  • Dongmei Li

摘要

The Smith form of matrices plays a significant role in the reduction of multidimensional systems and the equivalence of matrices. In this paper, the authors investigate the equivalence problem for two classes of multivariate polynomial matrices and their Smith forms. The authors derive some criteria on reducing these matrices to their Smith forms. Additionally, the authors provide an example to illustrate the main results.