| H-(反)对称矩阵的广义特征值反问题 |
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| 引用本文： | 燕列雅,任学明,王艳.H-(反)对称矩阵的广义特征值反问题[J].兰州理工大学学报,2012,38(3):139-142. |
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| 作者姓名： | 燕列雅 任学明 王艳 |
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| 作者单位： | 西安建筑科技大学理学院,陕西西安,710055 |
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| 基金项目： | 国家自然科学基金，陕西省教育厅科学研究计划基金 |
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| 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.
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| 关 键 词： | H-(反)对称矩阵 广义特征值 反问题 |
Inverse problems of generalized eigenvalue for H-(anti) symmetric mtrices |
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| YAN Lie-ya
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REN Xue-ming
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WANG Yan.Inverse problems of generalized eigenvalue for H-(anti) symmetric mtrices[J].Journal of Lanzhou University of Technology,2012,38(3):139-142. |
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| Authors: | YAN Lie-ya REN Xue-ming WANG Yan |
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| Institution: | (School of Science,Xi’an University of Arch.& Tech.,Xi’an 710055,China) |
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| Abstract: | 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-antisymmetric 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 above-mentioned feature of eigenvector of A-λB,the expression of solution to inverse problem AX=BXΛ of generalized eigenvalue of H-symmetric matrices and H-antisymmetric matrices were obtained. |
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| Keywords: | H-(anti)symmetric matrices generalized eigenvalue inverse problem |
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