二元多项式矩阵Smith型的进一步结果  

Some Further Results on the Smith Form of Bivariate Polynomial Matrices

作　　者：李冬梅[1] 梁芮 刘金旺[1] LI Dongmei;LIANG Rui;LIU Jinwang(School of Mathematics and Computations,Hunan University of Science and Technology,Xiangtan 411201)

机构地区：[1]湖南科技大学数学与计算科学学院,湘潭411201

出　　处：《系统科学与数学》2019年第12期1983-1997,共15页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11871207,11971161);湖南省研究生科研创新项目(CX2018B674)资助课题。

摘　　要：系统等价在二维系统研究中发挥重要作用,它与二元多项式矩阵等价问题密切相关.文章主要研究几类二元多项式矩阵与其Smith型等价问题,得到一些新的结果及这几类矩阵分别与其Smith型等价的判别准则.这些准则可以通过计算给定多项式矩阵的低一阶子式生成理想的Gr(o|")bner基进行检验.The equivalence of systems plays an important role in 2 D systems,which is closely related to the equivalence of bivariate polynomial matrices.In this paper,the Smith forms of several classes of bivariate polynomial matrices are investigated.Some new results and criteria on the equivalence of these matrices are obtained.These criteria are easily checked by computing the reduced Grobner basis of the ideal generated by the minors of lower order of the given matrix.

关 键 词：二维系统 二元多项式矩阵 矩阵等价 Smith型 

分 类 号：O151.21[理学—数学]