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| 环上矩阵的Moore-Penrose逆 | |
| 引用本文： | 岑建苗. 环上矩阵的Moore-Penrose逆[J]. 吉林大学学报(理学版), 2005, 43(4): 422-426 |
| 作者姓名： | 岑建苗 |
| 作者单位： | 宁波大学,数学系,浙江省,宁波,315211 |
| 基金项目： | 浙江省自然科学基金(批准号:102066). |
| 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Moore-Penrose逆. 给出环R上矩 阵的Moore-Penrose逆存在的几个充要条件. 得到了环R上矩阵A的Moore-Penrose逆 存在的充要条件是A有分解A=GDH, 其中D2=D=D*, (GD)*GD+I-D和DH(DH)*+I-D均可逆. |
| 关 键 词： | 环 矩阵 对称 Moore-Penrose逆 |
| 文章编号： | 1671-5489(2005)04-0422-05 |
| 收稿时间： | 2004-10-28 |
| 修稿时间： | 2004-10-28 |
On Moore-Penrose Inverses of Matrices over a Ring |
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| CEN Jian-miao. On Moore-Penrose Inverses of Matrices over a Ring[J]. Journal of Jilin University: Sci Ed, 2005, 43(4): 422-426 | |
| Authors: | CEN Jian-miao |
| Affiliation: | Department of Mathematics, Ningbo University, Ningbo 315211, Zhejiang Province, China |
| Abstract: | The Moore-Penrose inverses of matrices over a ring R with an involution * and unitary are (discussed). Some necessary and sufficient conditions for the existence of the Moore-Penrose inverse of matrices over a ring R are given. In particular, it is obtained that a necessary and sufficient condition for the existence of the Moore-Penrose inverse of a matrix A over a ring R is that A=GDH, where D~2=D=D~*,( (GD)~*GD+I-D ) and (DH(DH)~*+I-D) are invertible. |
| Keywords: | ring matrix *-symmetric Moore-Penrose inverse |
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