环上矩阵广义Moore-Penrose逆的存在性

岑建苗;

数学学报 ›› 2006, Vol. 49 ›› Issue (3) : 549-558.

PDF(345 KB)
PDF(345 KB)
数学学报 ›› 2006, Vol. 49 ›› Issue (3) : 549-558. DOI: 10.12386/A2006sxxb0069
论文

环上矩阵广义Moore-Penrose逆的存在性

    岑建苗;
作者信息 +

On Existence of the Generalized Moore-Penrose Inverses of Matrices over Ring

    Jian Miao CEN
Author information +
文章历史 +

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.

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.

关键词

*-对称 / 广义Moore-Penrose逆 / / 矩阵

引用本文

导出引用
岑建苗;. 环上矩阵广义Moore-Penrose逆的存在性. 数学学报, 2006, 49(3): 549-558 https://doi.org/10.12386/A2006sxxb0069
Jian Miao CEN. On Existence of the Generalized Moore-Penrose Inverses of Matrices over Ring. Acta Mathematica Sinica, Chinese Series, 2006, 49(3): 549-558 https://doi.org/10.12386/A2006sxxb0069
PDF(345 KB)

379

Accesses

0

Citation

Detail

段落导航
相关文章

/