摘要
本文研究了如下中心对称矩阵逆特征值问题:问题Ⅰ:已知X∈Rn×m,∧=diag(λ1,λ2,…λm),求A∈CSRn×n,使得‖AX-X∧‖=min.问题Ⅱ:已知A ∈Rn×n,求A～∈SE,使得‖A -A～‖=infA∈SE‖A -A～‖.其中SE是问题Ⅰ的解集.证明了问题Ⅰ、Ⅱ解的存在性,给出了问题Ⅰ解的通式及问题Ⅱ唯一解的表达式.
This paper discusses the following inverse eigenvalue problems for centro-symmetric matrics:Problem Ⅰ:GiveX∈R^(n×m)∧=diag(λ_1,λ_2,…λ_m),findA∈CSR^(n×n)such that‖AX-X∧‖=min.Problem Ⅱ:A~*∈R^(n×n),findA～∈S_E,so that‖A~*-A～‖=infA∈S_E‖A~*-A～‖. where S_E is the solution set of Problem Ⅰ.The existence of the solution for problems Ⅰ,Ⅱ and uniquness of the solution for problem Ⅱ are proved.The general form of S_E is given and the expression of A～ is presented.
出处
《扬州教育学院学报》
2004年第3期1-3,42,共4页
Journal of Yangzhou College of Education
关键词
中心对称矩阵
逆特征值问题
最小二乘解
centro-symmetric matrics
inverse eigenvalue problem
least-squares solution
