Extensions of G-outer inverses

Author:

Mosic Dijana1ORCID,Stanimirovic Predrag1ORCID,Ciric Miroslav1ORCID

Affiliation:

1. Faculty of Sciences and Mathematics, University of Niš, Niš, Serbia

Abstract

Our first objective is to present equivalent conditions for the solvability of the system of matrix equations ADA = A, D= 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.

Publisher

National Library of Serbia

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On G-Drazin partial order in rings;Acta Mathematica Hungarica;2024-05-08

2. A Zeroing Neural Network Approach for Calculating Time-Varying G-Outer Inverse of Arbitrary Matrix;IEEE Transactions on Neural Networks and Learning Systems;2024

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