GDMP-inverses of a matrix and their duals. Issue 19 (16th December 2022)

• Record Type: Journal Article
• Authors: Hernández, M.V.; Lattanzi, M.B.; Thome, N.
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 19(2022)
• Page Start: 3923
• Page End: 3935
• Publication Date: 2022-12-16
• Subjects: Generalized inverse -- Moore-Penrose inverse -- matrix equation -- G-Drazin inverse; 15A09 -- 15A24; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2020.1857678
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: This paper introduces and investigates a new class of generalized inverses, called GDMP-inverses (and their duals), as a generalization of DMP-inverses. GDMP-inverses are defined from G-Drazin inverses and the Moore-Penrose inverse of a complex square matrix. In contrast to most other generalized inverses, GDMP-inverses are not only outer inverses but also inner inverses. Characterizations and representations of GDMP-inverses are obtained by means of the core-nilpotent and the Hartwig-Spindelböck decompositions.