二元多项式矩阵Smith型等价问题  

On the Equivalence to the Smith Form of Bivariate Polynomial Matrices

作　　者：李冬梅[1] 梁芮 LI Dongmei;LIANG Rui(School of Mathematics and Computational Science,Hunan University of Science and Technology,Xiangtan 411201,Hunan,China)

机构地区：[1]湖南科技大学数学与计算科学学院,湖南湘潭411201

出　　处：《武汉大学学报（理学版）》2020年第3期224-232,共9页Journal of Wuhan University:Natural Science Edition

基　　金：国家自然科学基金(11871207)。

摘　　要：二维系统等价是多维系统研究中的重要问题,它常被转化为二元多项式矩阵的等价问题来研究。二元多项式矩阵与其Smith型等价是矩阵等价研究中的重要问题。本文主要研究几类二元多项式矩阵与其Smith型等价问题,给出二元多项式矩阵约化到其Smith型的一些结果和判别条件。这些条件可以通过计算矩阵既约子式的约化Gröbner基进行检验。The equivalence of two-dimensional systems is an important content of multidimensional systems,which is usually rep⁃resented by the bivariate polynomial matrices.Reducing a matrix to its Smith form is a very important study in the equivalence of matrices.In this paper we mainly investigate the reduction of several kinds of bivariate polynomial matrices to their Smith forms.Some new results and criteria are presented.These criteria can be verified easily by computing the Gröbner basis of the associated ideals.

关 键 词：二维系统 二元多项式矩阵 矩阵等价 Smith型 

分 类 号：O15[理学—数学]