| 环上矩阵广义Moore-Penrose逆的存在性 |
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| 引用本文： | 岑建苗.环上矩阵广义Moore-Penrose逆的存在性[J].数学学报,2006,49(3):549-558. |
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| 作者姓名： | 岑建苗 |
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| 作者单位： | 宁波大学数学系,宁波315211 |
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| 基金项目： | 国家自然科学基金项目（10471069）;浙江省自然科学基金项目（102066） |
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| 摘 要： | 讨论带有对合反自同构*有单位元的结合环R上矩阵的广义Moore-Penrose 逆,给出了环R上矩阵的广义Moore-Penrose逆存在的几个充要条件．特别,得到了环 R上矩阵A的关于M和N的广义Moore-Penrose逆存在的充要条件是A有分解A= GDH,其中D2=D,(MD)*=MD,(GD)*MGD+M(I-D)和DHN-1(DH)*+ (I-D)M-1均可逆．
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| 关 键 词： | 环 矩阵 *-对称 广义Moore-Penrose逆 |
| 文章编号： | 0583-1431（2006）03-0549-10 |
| 收稿时间： | 2004-11-26 |
| 修稿时间： | 2004-11-262005-03-08 |
On Existence of the Generalized Moore-Penrose Inverses of Matrices over Ring |
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| Jian Miao CEN.On Existence of the Generalized Moore-Penrose Inverses of Matrices over Ring[J].Acta Mathematica Sinica,2006,49(3):549-558. |
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| Authors: | Jian Miao CEN |
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| Institution: | Department of Mathematics, Ningbo University, Ningbo 315211, P. R. China |
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| Abstract: | The generalized Moore-Penrose inverses of matrices over a ring with an involution * and unitary are discussed. Some necessary and sufficient conditions for existence of the generalized Moore-Penrose inverse of matrices over a ring are given. In particular, it is obtained that a necessary and sufficient condition for existence of the generalized Moore-Penrose inverse with relation to M and N of a matrix A over a ring is that A = GDH, where D2 = D, (MD)* = MD, (GD)*MGD M(I-D) and DHN-1(DH)* (I-D)M-1 are invertible. |
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| Keywords: | ring matrix symmetric generalized Moore-Penrose inverse |
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