H-(反)对称矩阵的广义特征值反问题  

Inverse problems of generalized eigenvalue for H-(anti) symmetric matrices

作　　者：燕列雅[1] 任学明[1] 王艳[1] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055

出　　处：《兰州理工大学学报》2012年第3期139-142,共4页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(10971160);陕西省教育厅科学研究计划基金(11JK0503)

摘　　要：讨论H矩阵的性质,给出H-对称矩阵和H-反对称矩阵的结构,证明若x是H-对称矩阵或H-反对称矩阵A-λB的特征向量,则x是H-对称向量或H-反对称向量,或者x可以由H-对称向量及H-反对称向量线性表示,并根据A-λB的特征向量的上述特点,得到H-对称矩阵和H-反对称矩阵的广义特征值反问题AX=BXΛ解的表达式.Properties of H-matrices were discussed, the structures of H-symmetric and H-antisymmetric matrices were given, and it was proven that when x was an eigenvector of H-symmetric matrices or H-anti- symmetric matrices A-λB, x would be either an H-symmetric vector, or H-antisymmetric vector, or x could be expressed by linear combination of H-symmetric vector with H-antisymmetric vector. Based on a- bove-mentioned feature of eigenvector of A-λB, the expression of solution to inverse problem AX=BXA of generalized eigenvalue of H-symmetric matrices and H-antisymmetric matrices were obtained.

关 键 词：H-(反)对称矩阵 广义特征值 反问题 

分 类 号：O241.6[理学—计算数学]