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对称正交对称矩阵逆特征值问题

胡锡炎,张磊,周富照   

  1. 湖南大学应用数学系,湖南省计算中心,长沙交通学院 长沙 410082 ,长沙 410012 ,长沙 410076
  • 出版日期:2003-01-14 发布日期:2003-01-14

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.

THE INVERSE EIGENVALUE PROBLEM OF SYMMETRIC ORTHO-SYMMETRIC MATRICESTHE INVERSE EIGENVALUE PROBLEM OF SYMMETRIC ORTHO-SYMMETRIC MATRICES

  1. 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)
  • Online:2003-01-14 Published:2003-01-14
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.
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.
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