期刊论文

中文

计算数学

0254-7791

2003

25

3

281-292

10.3321/j.issn:0254-7791.2003.03.003

10171031:中国科学院项目（非规范项目） 50208004:中国科学院项目（非规范项目）

本校为第一机构

令R~(n×m)表示所有n×m阶实矩阵集合； OR~(n×m)表示所有n阶正交矩阵全体； A~+表示A的Moore-penrose广义逆；I_k表示k阶单位阵；SR~(n×m)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=(a_(ij))，B=(b_(ij))∈R~(n×m)， A*B表示A与B的Hadamard乘积，其定义为A*B=(a_(ij)b_(ij))．

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...