The E -relative m -weak group inverse

• David E. Ferreyra ^[1] ; Fabián E. Levis ^[1] ; Paola Moas ^[1] ; Dijana Mosić ^[2] ; Valentina Orquera ^[1]
  1. [1] Universidad Nacional de R´ıo Cuarto, Argentina
  2. [2] University of Niˇs, Serbia
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 69, Nº. 1, 2026, págs. 179-192
• Idioma: inglés
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• Resumen

  • 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.