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Volume 11
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Article

New Results on the Unimodular Equivalence of Multivariate Polynomial Matrices

by
Dongmei Li
and
Zuo Chen
*
School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan 411201, China
*
Author to whom correspondence should be addressed.
Mathematics 2023, 11(12), 2745; https://doi.org/10.3390/math11122745
Submission received: 14 May 2023 / Revised: 14 June 2023 / Accepted: 16 June 2023 / Published: 17 June 2023
(This article belongs to the Special Issue Matrix Equations and Their Algorithms Analysis)
Versions Notes

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 nD 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 multidimensional system; nD polynomial matrix; Smith normal form; unimodular equivalence

Share and Cite

MDPI and ACS Style

Li, D.; Chen, Z. New Results on the Unimodular Equivalence of Multivariate Polynomial Matrices. Mathematics 2023, 11, 2745. https://doi.org/10.3390/math11122745

AMA Style

Li D, Chen Z. New Results on the Unimodular Equivalence of Multivariate Polynomial Matrices. Mathematics. 2023; 11(12):2745. https://doi.org/10.3390/math11122745

Chicago/Turabian Style

Li, Dongmei, and Zuo Chen. 2023. "New Results on the Unimodular Equivalence of Multivariate Polynomial Matrices" Mathematics 11, no. 12: 2745. https://doi.org/10.3390/math11122745

APA Style

Li, D., & Chen, Z. (2023). New Results on the Unimodular Equivalence of Multivariate Polynomial Matrices. Mathematics, 11(12), 2745. https://doi.org/10.3390/math11122745

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