Mathematics

CLC number: O151.21

On the Zero Coprime Equivalence of Multivariate Polynomial Matrices

关于多元多项式矩阵的零互素等价

¹ School of Computer Science and Engineering, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China
² School of Mathematics and Statistics, Hunan University of Science and Technology, Xiangtan 411201, Hunan, China

^† Corresponding author. E-mail: dmli@hnust.edu.cn

Received: 30 January 2024

Abstract

The zero coprime system equivalence is one of important research in the theory of multidimensional system equivalence, and is closely related to zero coprime equivalence of multivariate polynomial matrices. We first discuss the relation between zero coprime equivalence and unimodular equivalence for polynomial matrices. Then, we investigate the zero coprime equivalence problem for several classes of polynomial matrices, some novel findings and criteria on reducing these matrices to their Smith normal forms are obtained. Finally, an example is provided to illustrate the main results.

摘要

零互素系统等价是多维系统等价理论中的重要研究内容之一，与多元多项式矩阵的零互素等价密切相关。本文首先讨论了多项式矩阵的零互素等价和幺模等价之间的关系。然后，我们研究了几类多项式矩阵的零互素等价问题，得到了将这些矩阵简化为其Smith型的一些新发现和准则。最后，通过一个例子来说明主要结果。