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
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