Research Article
Year 2025,
Volume: 38 Issue: 38, 82 - 89, 14.07.2025
Abstract
In this paper we investigate the g-Drazin invertibility of an anti-triangular block-operator matrix $\left(
\begin{array}{cc}
E&I\\
F&0
\end{array}
\right)$ with $F^{\pi}EF^d=0$ and $F^{\pi}EF^iE=0$ for all $i\in {\mathbb N}$. This generalizes the main results of [Guo, Zou and Chen, Hacet. J. Math. Stat., 49(3)(2020), 1134-1149] and [Chen and Sheibani, Appl. Math. Comput., 463(2024), 128368 (12 pp)] to a wider case.
References
- C. Bu, K. Zhang and J. Zhao, Representation of the Drazin inverse on solution of a class singular differential equations, Linear Multilinear Algebra, 59(8) (2011), 863-877.
- H. Chen and M. Sheibani, The g-Drazin inverses of special operator matrices, Oper. Matrices, 15(1) (2021), 151-162.
- H. Chen and M. Sheibani, The g-Drazin inverses of anti-triangular block operator matrices, Appl. Math. Comput., 463 (2024), 128368 (12 pp).
- C. Deng and Y. Wei, A note on the Drazin inverse of an anti-triangular matrix, Linear Algebra Appl., 431(10) (2009), 1910-1922.
- D. S. Djordjevic and P. S. Stanimirovic, On the generalized Drazin inverse and generalized resolvent}, Czechoslovak Math. J., 51 (2001), 617-634.
- D. S. Djordjevic and Y. Wei, Additive results for the generalized Drazin inverse, J. Aust. Math. Soc., 73(1) (2002), 115-125.
- L. Guo, H. Zou and J. Chen, The generalized Drazin inverse of operator matrices, Hacet. J. Math. Stat., 49(3) (2020), 1134-1149.
- Y. Liao, J. Chen and J. Cui, Cline's formula for the generalized Drazin inverse, Bull. Malays. Math. Sci. Soc. (2), 37(1) (2014), 37-42.
- M. Moucouf, $\mathcal P$-canonical forms and Drazin inverses of matrices, Filomat, 38(7) (2024), 2399-2417.
- D. Zhang, Representations for generalized Drazin inverse of operator matrices over a Banach space, Turkish J. Math., 40(2) (2016), 428-437.
- D. Zhang and D. Mosic, Explicit formulae for the generalized Drazin inverse of block matrices over a Banach algebra, Filomat, 32(17) (2018), 5907-5917.
- S. Zriaa and M. Moucouf, The explicit formulas of the Drazin inverse of matrices and its $n$th powers, Rend. Circ. Mat. Palermo (2), 73(2) (2024), 603-612.
Year 2025,
Volume: 38 Issue: 38, 82 - 89, 14.07.2025
Abstract
References
- C. Bu, K. Zhang and J. Zhao, Representation of the Drazin inverse on solution of a class singular differential equations, Linear Multilinear Algebra, 59(8) (2011), 863-877.
- H. Chen and M. Sheibani, The g-Drazin inverses of special operator matrices, Oper. Matrices, 15(1) (2021), 151-162.
- H. Chen and M. Sheibani, The g-Drazin inverses of anti-triangular block operator matrices, Appl. Math. Comput., 463 (2024), 128368 (12 pp).
- C. Deng and Y. Wei, A note on the Drazin inverse of an anti-triangular matrix, Linear Algebra Appl., 431(10) (2009), 1910-1922.
- D. S. Djordjevic and P. S. Stanimirovic, On the generalized Drazin inverse and generalized resolvent}, Czechoslovak Math. J., 51 (2001), 617-634.
- D. S. Djordjevic and Y. Wei, Additive results for the generalized Drazin inverse, J. Aust. Math. Soc., 73(1) (2002), 115-125.
- L. Guo, H. Zou and J. Chen, The generalized Drazin inverse of operator matrices, Hacet. J. Math. Stat., 49(3) (2020), 1134-1149.
- Y. Liao, J. Chen and J. Cui, Cline's formula for the generalized Drazin inverse, Bull. Malays. Math. Sci. Soc. (2), 37(1) (2014), 37-42.
- M. Moucouf, $\mathcal P$-canonical forms and Drazin inverses of matrices, Filomat, 38(7) (2024), 2399-2417.
- D. Zhang, Representations for generalized Drazin inverse of operator matrices over a Banach space, Turkish J. Math., 40(2) (2016), 428-437.
- D. Zhang and D. Mosic, Explicit formulae for the generalized Drazin inverse of block matrices over a Banach algebra, Filomat, 32(17) (2018), 5907-5917.
- S. Zriaa and M. Moucouf, The explicit formulas of the Drazin inverse of matrices and its $n$th powers, Rend. Circ. Mat. Palermo (2), 73(2) (2024), 603-612.
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory |
| Journal Section | Articles |
| Authors | |
| Early Pub Date | November 18, 2024 |
| Publication Date | July 14, 2025 |
| Submission Date | March 11, 2024 |
| Acceptance Date | October 30, 2024 |
| Published in Issue | Year 2025 Volume: 38 Issue: 38 |