New Results on the Unimodular Equivalence of Multivariate Polynomial Matrices

Dongmei Li and Zuo Chen ()
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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

Mathematics, 2023, vol. 11, issue 12, 1-15

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.

Keywords: multidimensional system; nD polynomial matrix; Smith normal form; unimodular equivalence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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