摘要
§1.问题的提出
矩阵反问题及逆特征值问题在工程中应用广泛,关于它们的研究已有了一些好的结果[1].[2,3,4]分别就反对称矩阵反问题和双对称矩阵反问题等进行了研究,双反对称矩阵在振动工程中有实际应用,但反问题尚未研究,本文将讨论这个问题.
This paper considers the following two problems: Problem A Given X, B e Rnxm, find A ∈ ABSn such thatAX = Bwhere ABSn is the set of all n x n anti-bisymmetric matrices. Problem B Given A ∈ Rnxn, find A e SE such thatwhere SE is the solution set of Problem A, || ?||F is the Frobenius norm.The necessary and sufficient conditions are studied for the set SE to be nonempty set. The general form of SE is given. For Problem B, the expression of the solution is provided.
出处
《数值计算与计算机应用》
CSCD
北大核心
2002年第2期111-120,共10页
Journal on Numerical Methods and Computer Applications
关键词
双反对称矩阵
反问题
解
逆特征值问题
Anti-bisymmetric matrices, matrices, matrix norm, optimal ap-proximation
