摘要
主要讨论广义逆问题A nX=λD nX,其中矩阵A n是由对称箭头矩阵加三对角矩阵合成的,矩阵D n是一个正定对角矩阵.研究如何由给定的正定矩阵D n,两个不同的实数λ,μ以及两个非零实向量X=(x 1,x 2,…,x n),Y=(y 1,y 2,…,y n)∈R n来构造矩阵A n,使得(λ,X)和(μ,Y)是矩阵对(A n,D n)的特征对.给出了该问题解的充要条件以及问题构造的算法,相应数值实例验证了结果.
The generalized inverse problem A nX=λD nX was discussed in this paper,in which the matrix A n was synthesized by a symmetric arrow matrix plus a tridiagonal matrix,and D n was a positive definite diagonal matrix.This paper mainly investigated how to reconstruct a matrix A n from the given positive definite matrix D n,two different real numbersλ,μ,and two non-zero real vectors X and Y∈R n,such that(λ,X)and(μ,Y)were characteristic pairs of matrix pairs(A n,D n).Finally,the necessary and sufficient conditions for the solution of the problem were solved and a constructive algorithm of the problem was provided,and illustrative numerical example was given to verify the results.
作者
雷英杰
郑志勇
LEI Yingjie;ZHENG Zhiyong(School of Science,North University of China,Taiyuan 030051,China)
出处
《安徽大学学报（自然科学版）》
CAS
北大核心
2020年第1期14-19,共6页
Journal of Anhui University(Natural Science Edition)
基金
国家自然科学基金资助项目(11602232)。
关键词
对称箭头矩阵
三对角矩阵
广义逆特征值
symmetric arrow matrix
tridiagonal matrix
generalized inverse eigenvalue
