Revista de la
Unión Matemática Argentina
The $E$-relative $m$-weak group inverse
David E. Ferreyra, Fabián E. Levis, Paola Moas, Dijana Mosić, and Valentina Orquera

Volume 69, no. 1 (2026), pp. 179–192    

Published online (final version): December 28, 2025

https://doi.org/10.33044/revuma.5181

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Abstract

We introduce the notion of the $m$-weak group inverse of a complex square matrix relative to an invertible Hermitian weight $E$. Several equivalent algebraic characterizations of this new type of generalized inverse are shown. In addition, various properties, representations, and characterizations involving the column space, null space, rank equalities, and projectors are presented. Finally, we use this new generalized inverse to solve a linear equation.

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