Further characterizations of the weak group inverse of matrices and the weak group matrix

Hui Yan; Hongxing Wang; Kezheng Zuo; Yang Chen; Hui Yan; Hongxing Wang; Kezheng Zuo; Yang Chen

doi:10.3934/math.2021542

AIMS Mathematics

2021, Volume 6, Issue 9: 9322-9341. doi: 10.3934/math.2021542

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Further characterizations of the weak group inverse of matrices and the weak group matrix

1.
School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China
2.
School of Mathematics and physics, Guangxi University for Nationalities, Nanning, 530006, China

Received: 09 April 2021 Accepted: 08 June 2021 Published: 22 June 2021
MSC : 15A09

This paper is devoted to consider some new characteristics and properties of the weak group inverse and the weak group matrix. First, we characterize the weak group inverse of a square matrix based on its range space and null space. Also several different characterizations of the weak group inverse are presented by projection and the Bott-Duffin inverse. Then by using the core-EP decomposition, we investigate the relationships between weak group inverse and other generalized inverses. And some new characterizations of weak group matrix are obtained.
- weak group inverse,
- weak group matrix,
- core-EP decomposition,
- rang space,
- null space
Citation: Hui Yan, Hongxing Wang, Kezheng Zuo, Yang Chen. Further characterizations of the weak group inverse of matrices and the weak group matrix[J]. AIMS Mathematics, 2021, 6(9): 9322-9341. doi: 10.3934/math.2021542

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Abstract

This paper is devoted to consider some new characteristics and properties of the weak group inverse and the weak group matrix. First, we characterize the weak group inverse of a square matrix based on its range space and null space. Also several different characterizations of the weak group inverse are presented by projection and the Bott-Duffin inverse. Then by using the core-EP decomposition, we investigate the relationships between weak group inverse and other generalized inverses. And some new characterizations of weak group matrix are obtained.

References

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