| 线性矩阵方程的埃尔米特广义反汉密尔顿半正定解 |
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| 引用本文： | 张忠志,胡锡炎,张磊.线性矩阵方程的埃尔米特广义反汉密尔顿半正定解[J].数学物理学报(A辑),2006,26(4):612-620. |
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| 作者姓名： | 张忠志 胡锡炎 张磊 |
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| 作者单位： | 东莞理工学院数学系，湖南大学数学与计量经济学院，湖南大学数学与计量经济学院 东莞 523808，长沙 410082，长沙 410082 |
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| 基金项目： | 国家自然科学基金(10571047)资助 |
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| 摘 要： | 利用埃尔米特广义反汉密尔顿半正定矩阵的表示定理,作者建立了线性矩阵方程在埃尔米特广义反汉密尔顿半正定矩阵集合中可解的充分必要条件,得到了解的一般表达式.对于逆特征值问题,也得到了可解的充分必要条件.对于任意一个 n 阶复矩阵,得到了相关最佳逼近问题解的表达式.
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| 关 键 词： | 埃尔米特广义反汉密尔顿半正定矩阵 线性矩阵方程
逆特征值问题 最佳逼近 |
| 文章编号： | 1003-3998(2006)04-612-09 |
| 收稿时间： | 2004-11-30 |
| 修稿时间： | 2006-01-08 |
On the Hermitian Generalized Anti-Hamiltonian Semi-definiteSolutions of Linear Matrix Equations |
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| Zhang Zhongzhi,Hu Xiyan,Zhang Lei.On the Hermitian Generalized Anti-Hamiltonian Semi-definiteSolutions of Linear Matrix Equations[J].Acta Mathematica Scientia,2006,26(4):612-620. |
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| Authors: | Zhang Zhongzhi Hu Xiyan Zhang Lei |
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| Institution: | Department of Mathematics, Dongguang University of Technology, Dongguan 523808 |
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| Abstract: | By means of the properties of Hermitian generalized anti-Hamiltonian semi-definite matrices, the authors give some necessary and sufficient conditions for the solvability of the linear matrix equation in Hermitian generalized anti-Hamiltonian semi-definite matrix set, and obtain a general expression of the solution for a solvable case. The authors also give some necessary and sufficient conditions of the solvability for inverse enginvalume problem of Hermitian generalized anti-Hamiltonian semi-definite matrices. For any n× n complex matrix, the authors derive the representation of its unique optimal approximation. |
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| Keywords: | Hermitian generalized anti-Hamiltonian semi-definite matrices Linear matrix equations Inverse enginvalume problems Optimal approximation |
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