广西师范大学学报（自然科学版） ›› 2015, Vol. 33 ›› Issue (3): 61-65.doi: 10.16088/j.issn.1001-6600.2015.03.009

• • 上一篇    下一篇

一类反三角矩阵的群逆和Drazin逆

刘喜富   

  1. 华东交通大学理学院,江西南昌330013
  • 收稿日期:2015-01-09 出版日期:2015-05-10 发布日期:2018-09-20
  • 通讯作者: 刘喜富(1984—),男,江西吉安人,华东交通大学讲师,博士。E-mail: liuxifu211@hotmail.com
  • 基金资助:
    国家自然科学基金资助项目(11426107);江西省科技厅青年科学基金资助项目(20142BAB211010)

The Group Inverses and Drazin Inverses of a Class of Anti-triangular Block Matrices

LIU Xi-fu   

  1. School of Science, East China Jiaotong University, Nanchang Jiangxi 330013, China
  • Received:2015-01-09 Online:2015-05-10 Published:2018-09-20

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摘要： 对于反三角矩阵M=PQI0的群逆和Drazin逆的研究,总是在块矩阵满足不同条件下进行的。本文在新的条件下获得了一些结论,即:当子块矩阵P可逆或ind(Q)≤1时,研究了M存在群逆的充要条件及群逆的表达式。同时根据这些结论,得到了当ind(P)≤1,PπQP=0和ind(P#QPP#)≤1时M的Drazin逆表达式,以及当PQQπ=0,Q2QD+QπPQπ可逆时M的Drazin逆表达式。

关键词: 群逆, Drazin逆, 反三角矩阵

Abstract: The research on the group inverse and Drazin inverse of the anti-triangular block matrix M=PQI0 was always done under some conditions for the sub-matrices. In this paper, some results are obtained under some new conditions, namely, when P is nonsingular or ind(Q)≤1, sufficient and necessary conditions for the existence of the group inverse of M are developed and the expressions of the group inverse of M are presented. Moreover, based on the above results, the representations for Drazin inverses of M are obtained under conditions ind(P)≤1, PπQP=0 and ind(P#QPP#)≤1, or on the conditions PQQπ=0 and Q2QD+QπPQπ are nonsingular.

Key words: group inverse, Drazin inverse, anti-triangular block matrix

中图分类号: 

  • O151.21
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