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arXiv · 2203.09086

Group inverse for anti-triangular block operator matrices

Huanyin Chen·Marjan Sheibani
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Abstract

We present the existence of the group inverse and its representation for the block operator matrix $\left( \begin{array}{cc} E&I\\ F&0 \end{array} \right)$ under the condition $FEF^{\pi}=0$. The group inverse for the anti-triangular block matrices with two identical subblocks under the same condition is thereby investigated. These extend the results of Zou, Chen and Mosi\'c (Studia Scient. Math. Hungar., 54(2017), 489--508), and Cao, Zhang and Ge (J. Appl. Math. Comput., 46(2014), 169--179).

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Huanyin Chen, Marjan Sheibani. 2022-03-17. Group inverse for anti-triangular block operator matrices. https://arxiv.org/abs/2203.09086

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