双对称矩阵逆特征值问题解存在的条件  

THE SOLVABILITY CONDITIONS FOR THE INVERSE EIGENVXLUE PROBLEM OF BISYMMETRIC MATRICES

作　　者：胡锡炎[1] 张磊 谢冬秀[1] 

机构地区：[1]湖南大学应用数学系 [2]湖南省计算所

出　　处：《计算数学》1998年第4期409-418,共10页Mathematica Numerica Sinica

摘　　要：This paper discuss the following two problems:Problem I. Given . Find A,such thatAX=XA,where BSRn×n is the set of all n × n bisymmetric matrices.Problem II. Given Find A SE such that where SE is the solution set of Problem I,is the Frobenius norm.In this paper, the sufficient and necessary conditions under which SE is nonempty are obtained. The general form of SE has been given. Then expression of the solution A of Problem II is presented.This paper discuss the following two problems:Problem I. Given . Find A,such thatAX=XA,where BSRn×n is the set of all n × n bisymmetric matrices.Problem II. Given Find A SE such that where SE is the solution set of Problem I,is the Frobenius norm.In this paper, the sufficient and necessary conditions under which SE is nonempty are obtained. The general form of SE has been given. Then expression of the solution A of Problem II is presented.

关 键 词：双对称矩阵 最佳逼近 特征值 逆特征值 解 

分 类 号：O241.6[理学—计算数学]