Geodesic
Extensions of G-outer inverses
Filomat, Tome 37 (2023) no. 22, p. 7407

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DOI

Our first objective is to present equivalent conditions for the solvability of the system of matrix equations ADA = A, DAB = B and CAD = C, where D is unknown, A, B, C are of appropriate dimensions, and to obtain its general solution in terms of appropriate inner inverses. Our leading idea is to find characterizations and representations of a subclass of inner inverses that satisfy some properties of outer inverses. A G-(B, C) inverse of A is defined as a solution of this matrix system. In this way, G-(B, C) inverses are defined and investigated as an extension of G-outer inverses. One-sided versions of G-(B, C) inverse are introduced as weaker kinds of G-(B, C) inverses and generalizations of one-sided versions of G-outer inverse. Applying the G-(B, C) inverse and its one-sided versions, we propose three new partial orders on the set of complex matrices. These new partial orders extend the concepts of G-outer (T, S)-partial order and one-sided G-outer (T, S)-partial orders.
DOI : 10.2298/FIL2322407M
Classification : 15A09, 15A24, 06A06, 65F05
Keywords: G-outer inverse, Left and right G-outer inverse, G-outer partial order, G-Drazin inverse 
Dijana Mosić; Predrag S Stanimirović; Miroslav Ćirić. Extensions of G-outer inverses. Filomat, Tome 37 (2023) no. 22, p. 7407 . doi: 10.2298/FIL2322407M
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     title = {Extensions of {G-outer} inverses},
     journal = {Filomat},
     pages = {7407 },
     year = {2023},
     volume = {37},
     number = {22},
     doi = {10.2298/FIL2322407M},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2322407M/}
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