双对称矩阵逆特征值问题解存在的条件 |
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引用本文: | 胡锡炎,张磊,谢冬秀.双对称矩阵逆特征值问题解存在的条件[J].计算数学,1998,20(4):409-418. |
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作者姓名: | 胡锡炎 张磊 谢冬秀 |
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作者单位: | [1]湖南大学应用数学系 [2]湖南省计算所 |
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摘 要: |
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关 键 词: | 双对称矩阵 最佳逼近 特征值 逆特征值 解 |
THE SOLVABILITY CONDITIONS FOR THE INVERSE EIGENVXLUE PROBLEM OF BISYMMETRIC MATRICES |
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Institution: | Hu Xi-Yan (Dept. of Appl. Math, Hunan University, Changsha)Zhang Lei (Hunan Computing Center, Changsha)Xie Dong-Xiu (Dept. of Appl. Math, Hunan University, Changsha) |
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Abstract: | This paper discuss the following two problems:Problem I. Given . Find A,such thatAX=XA,where BSRn×n is the set of all n × n bisymmetric matrices.Problem II. Given Find A SE such that where 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. Then expression of the solution A of Problem II is presented. |
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