Outer inverses and Jacobi type identities

被引：1

作者：

Bapat, Ravindra B. ^{[1
]}

Karantha, Manjunatha Prasad ^{[2
]}

Nandini, Nupur ^{[2
]}

Shenoy, Divya P. ^{[2
,3
]}

机构：

[1] Indian Stat Inst, Delhi Ctr, Theoret Stat & Math Unit, 7 SJS Sansanwal Marg, New Delhi 100016, India

[2] Manipal Univ, Dept Stat, Manipal 576104, Karnataka, India

[3] Manipal Univ, Manipal Inst Technol, Dept Math, Manipal 576104, Karnataka, India

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2018年 / 536卷

关键词：

Matrices over commutative ring; Outer inverse; Generalized inverse; Rao-regular matrix; Jacobi identity; Determinantal formula; GENERALIZED INVERSES; MATRICES;

D O I：

10.1016/j.laa.2017.09.025

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider matrices over a commutative ring and characterize the class of outer inverses for which Jacobi type identities can be extended. We obtain a necessary and sufficient condition for the existence of Rao-regular Drazin inverse in terms of sum of principal minors of A(k) for some k. Also, we obtain determinantal formula for the Rao-regular Drazin inverse. Conjectures are formulated which give expressions for outer inverse and the conjectures are proved in some special cases. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：274 / 294

页数：21

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