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The Core Inverse of a Product and \(2\times 2\) Matrices

  • Yuanyuan Ke
  • Long Wang
  • Jianlong ChenEmail author
Article

Abstract

The core inverse of a complex matrix was first introduced by Baksalary and Trenkler. In 2014, Rakić extended the notion of the core inverse to the ring with involution. In this paper, equivalent conditions for the existence of the core inverse for a product of three elements are characterized under some conditions. As applications, the existence and representation for the core inverse of a lower triangular matrix \(T=\begin{bmatrix} a&0\\ b&d \end{bmatrix}\) and a \(2\times 2\) matrix \(M=\begin{bmatrix} a&c \\ b&d \end{bmatrix}\) are considered.

Keywords

Generalized inverse Group inverse Core inverse Dual core inverse Matrix over a ring 

AMS Subject Classification

15A09 16S50 

Notes

Acknowledgements

We would like to express our sincere appreciation to the referees for valuable comments and suggestions. The research was supported by the Foundation of Graduate Innovation Program of Jiangsu Province (No. KYLX\(_{-}\)0080), Natural Science Fund for Colleges and Universities in Jiangsu Province (No. 15KJB110021), the NSFC (No. 11371089), the NSF of Jiangsu Province (No. BK20141327).

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of MathematicsSoutheast UniversityNanjingChina
  2. 2.Department of MathematicsTaizhou UniversityTaizhouChina

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