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G-Drazin inverse combined with inner inverse

Published 15 Feb 2024 in math.NA and cs.NA | (2402.09699v1)

Abstract: This paper introduces new classes of generalized inverses for square matrices named GD1, and the dual, called 1GD inverse. In addition, we discuss a few characterizations and representations of these inverses. The explicit expressions of these inverses have been established via core-nilpotent decomposition. Further, we introduce a binary relation for GD1 inverse and 1GD inverse, along with a few derived properties.

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