| 埃尔米特反自反矩阵左右逆特征值问题的可解条件 |
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| 引用本文： | 王江涛,刘能东.埃尔米特反自反矩阵左右逆特征值问题的可解条件[J].东莞理工学院学报,2009,16(5):1-5. |
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| 作者姓名： | 王江涛 刘能东 |
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| 作者单位： | 1. 华南理工大学,理学院,广州,510641;东莞理工学院,计算机学院,广东东莞,523808
2. 东莞理工学院,计算机学院,广东东莞,523808 |
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| 基金项目： | 国家自然科学基金，北京市教学名师建设项目 |
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| 摘 要： | 利用埃尔米特反自反矩阵的表示定理,推导了其最小二乘问题的表达式,并给出了左右逆特征值问题可解的充分必要条件及其解的一般表达式。最后对任意一个阶复矩阵,给出了相关的最佳逼近问题解的表达形式。
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| 关 键 词： | 埃尔米特反自反矩阵 左右逆特征值 最小二乘解 最佳逼近 |
The Conditions for the Left and Right Inverse Eigenvalue Problem of Hermitian-Antireflexive Matrix |
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| WANG Jiang-tao,LIU Neng-dong.The Conditions for the Left and Right Inverse Eigenvalue Problem of Hermitian-Antireflexive Matrix[J].Journal of Dongguan Institute of Technology,2009,16(5):1-5. |
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| Authors: | WANG Jiang-tao LIU Neng-dong |
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| Institution: | WANG Jiang-tao~(1,2) LIU Neng-dong~2 (1.College of science South China University of Technology,Guangzhou 510641,China,2.Department of Mathematics Dongguan University of Technology,Dongguan 523808,China) |
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| Abstract: | By means of the properties of the Hermitian-Antireflexive matrix,the least-square solution of the left and right inverse eigenvalue problem of Hermitian-Antireflexive matrix is derived and the necessary and sufficient conditions of the problem are considered and then the general expression of the solution is presented.Finally,for any given n order of complex matrix,the expression of the solution for relevant optimal approximate problem is presented. |
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| Keywords: | Hermitian Antireflexive matrix left and right inverse eigenvalue least-square optimal approximation |
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