| 域上保持对称矩阵群逆的线性算子 |
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| 引用本文： | 卜长江,井世丽,王贵艳. 域上保持对称矩阵群逆的线性算子[J]. 哈尔滨工程大学学报, 2007, 28(10): 1188-1190 |
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| 作者姓名： | 卜长江 井世丽 王贵艳 |
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| 作者单位： | 哈尔滨工程大学,理学院,黑龙江,哈尔滨,150001;哈尔滨工程大学,理学院,黑龙江,哈尔滨,150001;哈尔滨工程大学,理学院,黑龙江,哈尔滨,150001 |
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| 基金项目： | 哈尔滨工程大学校科研和教改项目 |
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| 摘 要： | 设F是一个特征为2的域,|F|＞4,令Mn(F),Sn(F),分别为全矩阵空间和对称矩阵空间.讨论了在特征为2的情况下从Sn(F)到Mn(F)上保持对称矩阵群逆的线性算子的表示形式问题.给出了在特征为2的情况下从Sn(F)到Sn(F)保持对称矩阵群逆的线性算子的表示形式.研究的保持问题不仅在数学理论上有着广泛研究,而且在系统控制、量子力学、微分几何、数理统计等领域有着广泛的实际应用背景.
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| 关 键 词： | 域 矩阵的群逆 线性算子 对称矩阵 |
| 文章编号： | 1006-7043（2007）10-1188-03 |
| 修稿时间： | 2006-11-15 |
Linear maps preserving group inverse of symmetric matrices over field |
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| BU Chang-jiang,JING Shi-li,WANG Gui-yan. Linear maps preserving group inverse of symmetric matrices over field[J]. Journal of Harbin Engineering University, 2007, 28(10): 1188-1190 |
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| Authors: | BU Chang-jiang JING Shi-li WANG Gui-yan |
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| Affiliation: | College of Science, Harbin Engineering University, Harbin 150001, China |
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| Abstract: | Let F be a field of chF=2,|F|>4,and Mn(F),Sn(F)be the spaces of all matrices and symmetric matrices respectively over F.In this paper we determine the forms of linear maps from Sn(F) to Mn(F) preserving group inverse of symmetric matrices under chF=2 and also determine the forms of linear maps from Sn(F) to itself preserving group inverses of symmetric matrices under chF=2.The problem we are study not only be developed deeply in mathematic theory,but also be applied extensively on practice such as system control,quantum mechanics,differential geometry and mathematical statistics,etc. |
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| Keywords: | field group inverse linear operator symmetric matrices |
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