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| 对称正交对称矩阵逆特征值问题 | |
| 引用本文： | 胡锡炎,张磊,周富照. 对称正交对称矩阵逆特征值问题[J]. 计算数学, 2003, 25(1): 13-22 |
| 作者姓名： | 胡锡炎 张磊 周富照 |
| 作者单位： | 1. 湖南大学应用数学系,长沙,410082 2. 湖南省计算中心,长沙,410012 3. 长沙交通学院,长沙,410076 |
| 基金项目： | 国家自然科学基金资助项目(19871024) |
| 摘 要： | Let P∈ Rn×n such that PT = P, P-1 = PT.A∈Rn×n is termed symmetric orthogonal symmetric matrix ifAT = A, (PA)T = PA.We denote the set of all n × n symmetric orthogonal symmetric matrices byThis paper discuss the following two problems:Problem I. Given X ∈ Rn×m, A = diag(λ1,λ 2, ... ,λ m). Find A SRnxnP such thatAX =XAProblem II. Given A ∈ Rnδn. Find A SE such thatwhere 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. The expression of the solution A* of Problem II is presented. We have proved that some results of Reference [3] are the special cases of this paper. |
| 关 键 词： | 对称正交对称矩阵 逆特征值 Moore－penrose广义逆 Frobenius范数 |
| 修稿时间： | 2000-10-26 |
THE INVERSE EIGENVALUE PROBLEM OF SYMMETRIC ORTHO-SYMMETRIC MATRICESTHE INVERSE EIGENVALUE PROBLEM OF SYMMETRIC ORTHO-SYMMETRIC MATRICES |
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| Hu Xiyan. THE INVERSE EIGENVALUE PROBLEM OF SYMMETRIC ORTHO-SYMMETRIC MATRICESTHE INVERSE EIGENVALUE PROBLEM OF SYMMETRIC ORTHO-SYMMETRIC MATRICES[J]. Mathematica Numerica Sinica, 2003, 25(1): 13-22 | |
| Authors: | Hu Xiyan |
| Affiliation: | Hu Xiyan (De.pt. of Appl. Math, Hunan University, Changsha, 410082)Zhang Lei (Hunan Computing Center, Changsha, 410012)Zhou Fuzhao (Changsha Communications University, Changsha, 410076) |
| Abstract: | |
| Keywords: | Symmetric ortho-symmetric matrices matrix norm optimal approximation |
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