Revisiting the m-weak core inverse

Jinyong Wu; Wenjie Shi; Sanzhang Xu; Jinyong Wu; Wenjie Shi; Sanzhang Xu

doi:10.3934/math.20241054

AIMS Mathematics

2024, Volume 9, Issue 8: 21672-21685. doi: 10.3934/math.20241054

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Research article

Revisiting the m-weak core inverse

1.
School of Mathematics and Physics, Wenzhou University, Wenzhou 325035, China
2.
Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, 223003, China

Received: 05 March 2024 Revised: 05 June 2024 Accepted: 20 June 2024 Published: 08 July 2024
MSC : 15A09

The $ m $-weak core inverse of a complex matrix was introduced by D. E. Ferreyra and Saroj B. Malik in 2024. We have revisited this inverse by using the inverse along two matrices, that is, we have proved that the $ m $-weak core inverse of a complex matrix coincides with the inverse along two complex matrices. Moreover, the necessary and sufficient conditions of the $ m $-weak core inverse of a complex matrix have been obtained. The one-sided $ m $-weak core inverse has been introduced by using the core-EP (EP means Equal Prohection) inverse of $ A $.
- the inverse along two matrices,
- index,
- the $ m $-weak core inverse,
- core-EP inverse,
- complex matrix
Citation: Jinyong Wu, Wenjie Shi, Sanzhang Xu. Revisiting the m-weak core inverse[J]. AIMS Mathematics, 2024, 9(8): 21672-21685. doi: 10.3934/math.20241054

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Abstract

The $ m $-weak core inverse of a complex matrix was introduced by D. E. Ferreyra and Saroj B. Malik in 2024. We have revisited this inverse by using the inverse along two matrices, that is, we have proved that the $ m $-weak core inverse of a complex matrix coincides with the inverse along two complex matrices. Moreover, the necessary and sufficient conditions of the $ m $-weak core inverse of a complex matrix have been obtained. The one-sided $ m $-weak core inverse has been introduced by using the core-EP (EP means Equal Prohection) inverse of $ A $.

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