Revisiting of the BT-inverse of matrices

Wanlin Jiang; Kezheng Zuo; Wanlin Jiang; Kezheng Zuo

doi:10.3934/math.2021158

AIMS Mathematics

2021, Volume 6, Issue 3: 2607-2622. doi: 10.3934/math.2021158

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Research article

Revisiting of the BT-inverse of matrices

Wanlin Jiang ,
Kezheng Zuo ^,

School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China

Received: 14 October 2020 Accepted: 21 December 2020 Published: 28 December 2020
MSC : 15A09

In this paper, we discuss different characteristics of the BT-inverse of a square matrix introduced by Baksalary and Trenkler [On a generalized core inverse, Appl. Math. Comput., 236 (2014), 450-457]. While the BT-inverse is defined by a expression, we present some necessary and sufficient conditions for a matrix to be the BT-inverse. Then we give a canonical form of BT-inverse and investigate the relationships between BT-inverse and other generalized inverses by Core-EP decomposition. Some properties of BT-inverse concerned with some classes of special matrix are identified by Core-EP decomposition. Furthermore new representations of BT-inverse are given by the maximal classes of matrices.
- BT-inverse,
- Core-EP decomposition,
- Hartwig-Spindelbock decomposition
Citation: Wanlin Jiang, Kezheng Zuo. Revisiting of the BT-inverse of matrices[J]. AIMS Mathematics, 2021, 6(3): 2607-2622. doi: 10.3934/math.2021158

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Abstract

In this paper, we discuss different characteristics of the BT-inverse of a square matrix introduced by Baksalary and Trenkler [On a generalized core inverse, Appl. Math. Comput., 236 (2014), 450-457]. While the BT-inverse is defined by a expression, we present some necessary and sufficient conditions for a matrix to be the BT-inverse. Then we give a canonical form of BT-inverse and investigate the relationships between BT-inverse and other generalized inverses by Core-EP decomposition. Some properties of BT-inverse concerned with some classes of special matrix are identified by Core-EP decomposition. Furthermore new representations of BT-inverse are given by the maximal classes of matrices.

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