New Results on the Equivalence of Bivariate Polynomial Matrices

作     者：ZHENG Xiaopeng LU Dong WANG Dingkang XIAO Fanghui ZHENG Xiaopeng;LU Dong;WANG Dingkang;XIAO Fanghui

作者机构：KLMMAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China School of MathematicsSouthwest Jiaotong UniversityChengdu 610031China MOE-LCSMSchool of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2023年第36卷第1期

页      面：77-95页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China under Grant Nos.12171469,12001030 and 12201210 the National Key Research and Development Program under Grant No.2020YFA0712300 the Fundamental Research Funds for the Central Universities under Grant No.2682022CX048 

主　　题：Bivariate polynomial matrix matrix equivalence smith form 

摘      要：This paper investigates the equivalence problem of bivariate polynomial matrices.A necessary and sufficient condition for the equivalence of a square matrix with the determinant being some power of a univariate irreducible polynomial and its Smith form is ***,the authors present an algorithm that reduces this class of bivariate polynomial matrices to their Smith forms,and an example is given to illustrate the effectiveness of the *** addition,the authors generalize the main result to the non-square case.