On the Zero Coprime Equivalence of Multivariate Polynomial Matrices  

关于多元多项式矩阵的零互素等价

作　　者：CHEN Zuo LI Dongmei GUO Xu 陈作;李冬梅;郭旭(湖南科技大学计算机科学与工程学院,湖南湘潭411201;湖南科技大学数学与统计学院,湖南湘潭411201)

机构地区：[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

出　　处：《Wuhan University Journal of Natural Sciences》2025年第1期32-42,共11页武汉大学学报(自然科学英文版)

基　　金：Supported by the National Natural Science Foundation of China(12271154);the Natural Science Foundation of Hunan Province(2022JJ30234);the Postgraduate Scientific Research Innovation Project of Hunan Province(CX20231032)。

摘　　要：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.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。

关 键 词：multidimensional system multivariate polynomial matrix zero coprime equivalence unimodular equivalence Smith normal form 

分 类 号：O151.21[理学—数学]