| 一类矩阵方程的Hermite广义Hamilton解及其最佳逼近 |
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| 引用本文： | 李迎春,刘志宏. 一类矩阵方程的Hermite广义Hamilton解及其最佳逼近[J]. 高师理科学刊, 2010, 30(3). DOI: 10.3969/j.issn.1007-9831.2010.03.003 |
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| 作者姓名： | 李迎春 刘志宏 |
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| 作者单位： | 红河学院,数学学院,云南,蒙自,661100 |
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| 基金项目： | 云南省教育厅科研立项基金,红河学院博、硕启动项目 |
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| 摘 要： | 利用矩阵的广义奇异值分解定理,得到了矩阵方程AHXA=B存在Hermite广义Hamilton解的充分必要条件,并在有解时得到了通解的表达式,同时得到了相应解集中与已知矩阵最佳逼近的Hermite广义Hamilton解和最小范数解.
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| 关 键 词： | 矩阵方程 Hermite广义Hamilton矩阵 最佳逼近解 最小范数解 |
Hermite generalized Hamiltonian solutions for matrix equation and its optimal approximation |
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| LI Ying-chun,LIU Zhi-hong. Hermite generalized Hamiltonian solutions for matrix equation and its optimal approximation[J]. Journal of Science of Teachers＇College and University, 2010, 30(3). DOI: 10.3969/j.issn.1007-9831.2010.03.003 |
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| Authors: | LI Ying-chun LIU Zhi-hong |
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| Affiliation: | LI Ying-chun,LIU Zhi-hong(School of Mathematics,Honghe University,Mengzi 661100,China) |
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| Abstract: | Applying the generalized singular value decomposition of matrices,the necessary and sufficient conditions for the existence and the expression for the Hermite generalized Hamiltonian solutions of the matrix equation AHXA=Bwas derived.In addition,in Hermite generalized Hamiltonian solutions set of the equation,the expressions of the optimal approximation solutions and of the minimum norm solutions to the given matrix was obtained. |
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| Keywords: | matrix equation Hermite generalized Hamiltonian matrices optimal approximation solutions minimum norm solution |
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