对称自正交相似矩阵的逆特征值问题  

INVERSE EIGENPROBLEM OF SYMMETRIC AND SELF-ORTHOGONAL SIMILAR MATRICES

作　　者：盛炎平[1] 王来生[1] 

机构地区：[1]中国农业大学理学院

出　　处：《高等学校计算数学学报》2004年第4期351-357,共7页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1引言 对称自正交相似矩阵在结构力学及土木工程等中有实际应用,在许多实际问题中会遇到其逆特征值问题.因此研究此问题是有意义的.A ∈ R2k×2k is symmetric and self-orthogonal similar matrix, ifJAJT = AT,AT = A,whereWe denoted the set of all symmetric and self-orthogonal similar matrices by Jn×n(n = 2k). In this paper, the following two problems are discussed:Problem Ⅰ Let X ∈ Rn×m, A = diag(λ1,λ2,...,λm) be given, find A ∈ Jn×n such thatAX = A∧.Problem Ⅱ Let C ∈ Rn×m be given, find A ∈ SE such thatwhere SE is the solution set of Problem Ⅰ , || · || is the Probenius norm.For problem Ⅰ , the general form of SEis given and for problem Ⅱ , the expressionof the solution is provided.

关 键 词：逆特征值问题 相似矩阵 对称 正交 

分 类 号：O151[理学—数学]