符号非奇异的3阶Toeplitz符号模式  

Sign non-singular Toeplitz sign patterns of order 3

作　　者：田岩 黎竹璐 王爱伟 TIAN Yan;LI Zhulu;WANG Aiwei(School of Mathematics,Liaoning Normal University,Dalian 116081,China;School of Economics,Liaoning University of International Business and Economics,Dalian 116052,China)

机构地区：[1]辽宁师范大学数字学院,辽宁大连116081 [2]辽宁对外经贸学院经济学院,辽宁大连116052

出　　处：《辽宁师范大学学报（自然科学版）》2024年第4期441-448,共8页Journal of Liaoning Normal University:Natural Science Edition

基　　金：辽宁师范大学研究生教育教学改革研究项目(YJSJG202419);教育部产学合作协同育人项目(230804-092233033)。

摘　　要：基于Toeplitz矩阵的结构特点,考虑了Toeplitz符号模式.借助组合矩阵论以及图论的理论,研究了3阶Toeplitz符号模式是否符号非奇异问题.利用置换相似,将3阶Toeplitz符号模式进行分类讨论.证明了3阶Toeplitz符号模式符号非奇异的充分必要条件,给出了符号非奇异的3阶Toeplitz符号模式的具体结构.研究丰富了组合矩阵理论,为符号模式符号非奇异的研究提供了方法和思路.Based on the structural characteristics of Toeplitz matrices,Toeplitz sign patterns are studied.By using the graph theory and the combinatorial matrices theory,this paper studies Toeplitz sign patterns of order 3 which are whether sign non-singular.Utilizing permutation similarity,Toeplitz sign patterns of order 3 are classified and discussed.A sufficient and necessary condition on Toeplitz sign patterns of order 3 that are sign non-singular is proved,the concrete structures of sign non-singular Toeplitz sign patterns of order 3 are given.The research of this paper enriches the combinatorial matrix theory,the methods and ideas are provided for the study of non-singular sign patterns.

关 键 词：符号模式 Toeplitz符号模式 符号非奇异 

分 类 号：O151.21[理学—数学]