An extension of the MPD and MP weak group inverses

Dijana Mosić, Daochang Zhang and Predrag S. Stanimirović

Applied Mathematics and Computation, 2024, vol. 465, issue C

Abstract: Combining the Moore-Penrose (MP) inverse with m-weak group inverse (m-WGI) in an appropriate way, we solve certain systems of equations and establish a novel class of generalized inverses, which is called the Moore-Penrose m-WGI (MP-m-WGI). Since the weak group inverse (WGI) and Drazin inverse are particular instances of the m-WGI family, it clearly follows that MP weak group (MPWG) inverse and MPD inverse are subclasses of the MP-m-WGI. We present a number of effective representations and characterizations for the MP-m-WGI. As corollaries, we propose new generalized inverses and validate some known properties and representations of the MPD inverse. The MP-2-WGI is considered as one important kind of the MP-m-WGI. Continuity of the MP-m-WGI is studied too. Solvability of a few linear equations is proved and general solutions are expressed as expressions which include the MP-m-WGI.

Keywords: m-WGI; Moore-Penrose inverse; MP weak group inverse; MPD inverse (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:465:y:2024:i:c:s0096300323005982

DOI: 10.1016/j.amc.2023.128429

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