| 任意除环上矩阵的广义逆 |
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| 引用本文： | 刘永辉,朱超,陈果良.任意除环上矩阵的广义逆[J].数学物理学报(A辑),2005,25(6):770-776. |
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| 作者姓名： | 刘永辉 朱超 陈果良 |
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| 作者单位： | [1]中国科学院数学与系统科学研究院计算数学与科学工程计算研究所,北京100080 [2]上海金融学院,上海201209 [3]Department of Mathematics, Dayne State University, Detroit, MI, 48202, USA [4]华东师范大学数学系,上海200062 |
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| 基金项目： | 国家自然科学基金（10371044）资助 |
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| 摘 要： | 该文使用投影算子方法研究任意除环上矩阵的广义逆, 建立了具有指定值域和零空间的{2} 逆的刻划和表示理论. 作为应用, 获得了带有对合函数的Moore Penrose逆, 群逆和Dra zin逆的一些新的表式.
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| 关 键 词： | 除环 广义逆 |
| 文章编号： | 1003-3998(2005)06-770-07 |
| 收稿时间： | 2003-10-31 |
| 修稿时间： | 2004-09-10 |
Generalized Inverses of Matrices on an Arbitrary Division Ring |
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| LIU Yong-Hui,SHU Chao,CHEN Guan-Liang.Generalized Inverses of Matrices on an Arbitrary Division Ring[J].Acta Mathematica Scientia,2005,25(6):770-776. |
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| Authors: | LIU Yong-Hui SHU Chao CHEN Guan-Liang |
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| Institution: | 1.Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080;2.Shanghai Finance University, Shanghai 201209;3.Department of Mathematics, Dayne State University, Detroit, MI, 48202, USA; 4.Department of Mathematics, East China Normal University, Shanghai 200062 |
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| Abstract: | In this paper, generalized inverses of matrices on an arbitrary division ring are studied by using projector operator. The characterization and representation theory of {2} inverses with prescribed range and null space are established. As an application, some new representation forms of p M-P inverse, group inverse and Drazin inverse are obtained. |
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| Keywords: | Division ring Generalized inverse A_(T S)~(2) M-P inverse Group inverse Drazin inverse |
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