复区间矩阵的Gerschgorin圆盘定理及正则性条件  

The Gerschgorin Disk Theorem and Regularity Conditions for Complex Interval Matrices

作　　者：成龙 夏丹丹 李耀堂[2] Cheng Long;Xia Dandan;Li Yaotang(School of Mathematics and Computer Science,Chongqing University of International Business and Economics,Chongqing 401520,China;School of Mathematics and Statistics,Yunnan University,Kunming 650091,China)

机构地区：[1]重庆对外经贸学院数学与计算机学院,重庆401520 [2]云南大学数学与统计学院,昆明650091

出　　处：《数学理论与应用》2024年第1期109-121,共13页Mathematical Theory and Applications

基　　金：国家自然科学基金(No.11861077);重庆对外经贸学院科学研究项目基金(Nos.KYKJ202208,KYZK202311)资助。

摘　　要：本文将矩阵特征值的Gerschgorin圆盘定理推广到复区间矩阵,给出复区间矩阵特征值的Gerschgorin圆盘区域,并证明所给复区间矩阵特征值的Gerschgorin圆盘区域包含于已有的复区间矩阵特征值的Gerschgorin方盘区域.最后,应用复区间矩阵特征值的Gerschgorin圆盘定理得到复区间矩阵正则的两个新的充分条件.In this paper,the Gerschgorin disk theorem on eigenvalues of complex matrices is generalized to complex interval matrices,in which the Gerschgorin disk regions of eigenvalues of complex interval matrices are presented.It is showed that the Gerschgorin disk regions are contained in the Gerschgorin square regions for eigenvalues of complex interval matrices.Then,two new sufficient conditions for the regularity of complex interval matrices are obtained by applying the Gerschgorin disk theorem of complex interval matrices.

关 键 词：复区间矩阵 特征值 Gerschgorin圆盘定理 正则性 

分 类 号：O151.21[理学—数学]