线性流形上对称正交对称矩阵逆特征值问题  

THE INVERSE EIGENVALUE PROBLEMS OF SYMMETRIC ORTHO-SYMMETRIC MATRICES ON THE LINEAR MANIFOLD

作　　者：周富照[1] 胡锡炎[2] 张磊 

机构地区：[1]长沙交通学院信息与计算科学系,长沙410076 [2]湖南大学应用数学系,长沙410082 [3]湖南省计算中心,长沙410012

出　　处：《计算数学》2003年第3期281-292,共12页Mathematica Numerica Sinica

基　　金：国家自然科学基金资助项目(项目号:10171031和 50208004)

摘　　要：1.引言 令Rn×m表示所有n×m阶实矩阵集合;ORn×n表示所有n阶正交矩阵全体;A+表示A的Moore-penrose广义逆;Ik表示k阶单位阵;SRn×n表示n阶实对称矩阵的全体;rank(A)表示A的秩;‖@‖是矩阵的Frobenius范数;对A=(aij),B=(bij)∈Rn×m,A*B表示A与B的Hadamard乘积,其定义为A*B=(aijbij).Let P ∈ ORn×n such that PT = P, and Where is the set of all n × n symmetric ortho-symmetric matrices. In this paper, we discuss the following problems: Problem I0. Given A = diag, diag and let Y = ZΛ. in S. Find A ∈S such that AX = XΓ. Problem Ⅰ. Given X,B ∈ Rn×m. Find A∈S such that ||AX-B|| = min. Problem Ⅱ. Given A ∈ Rn×n. Find .A* ∈ SE such that Where ||·|| is the Frobenius norm, and SE is the solution set of Problem Ⅰ. In this paper the general representation of SE has been given. The necessary and sufficient conditions have been presented for Problem I0. For Problem Ⅱ the expression of the solution has been provided.

关 键 词：线性流形 对称正交对称矩阵 逆特征值问题 矩阵范数 逼近解 算法 

分 类 号：O151.21[理学—数学]