On the Drazin inverse of anti-triangular block matrices

Daochang Zhang; Dijana Mosić; Liangyun Chen; Daochang Zhang; Dijana Mosić; Liangyun Chen

doi:10.3934/era.2022124

Electronic Research Archive

2022, Volume 30, Issue 7: 2428-2445. doi: 10.3934/era.2022124

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Research article

On the Drazin inverse of anti-triangular block matrices

1.
School of Mathematics and Statistics, Northeast Normal University, Changchun, China
2.
College of Sciences, Northeast Electric Power University, Jilin, China
3.
Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000 Niš, Serbia

Received: 28 August 2021 Revised: 17 January 2022 Accepted: 20 January 2022 Published: 29 April 2022

Our aim is to present new expressions for the Drazin inverse of anti-triangular block matrices under some circumstances. Applying the established new formulae for anti-triangular block matrices, we derive explicit representations for the Drazin inverse of a $ 2\times2 $ complex block matrix under corresponding assumptions. We extend several well known results in the literature in this way.
- Drazin inverse,
- block matrix,
- anti-triangular block matrix,
- index
Citation: Daochang Zhang, Dijana Mosić, Liangyun Chen. On the Drazin inverse of anti-triangular block matrices[J]. Electronic Research Archive, 2022, 30(7): 2428-2445. doi: 10.3934/era.2022124

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Abstract

Our aim is to present new expressions for the Drazin inverse of anti-triangular block matrices under some circumstances. Applying the established new formulae for anti-triangular block matrices, we derive explicit representations for the Drazin inverse of a $ 2\times2 $ complex block matrix under corresponding assumptions. We extend several well known results in the literature in this way.

References

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