Research Article

The (B, C)-core inverse of rectangular matrices

Published in: Quaestiones Mathematicae
Volume 47 , issue 12 , 2024 , pages: 2429–2446

DOI: 10.2989/16073606.2024.2374776

Author(s): Huihui Zhu Hefei University of Technology, China , Daihan Xu Hefei University of Technology, China , Pedro Patrício Universidade do Minho, Portugal , Dijana Mosić University of Niš, Serbia

Keywords: 15A09 , (B , C)-core inverses , Moore–Penrose inverses , matrix equations

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Abstract

Let A be an m × n complex matrix and let B, C be n × m complex matrices. The main purpose of this article is to derive several new properties of the (B, C)-core inverse. Also, we introduce and investigate the dual (B, C)-core inverse in the context of rectangular matrices. The connection between (dual) (B, C)-core inverses and other generalized inverses is given. Finally, the minimum norm solution and least square solution to the equation are expressed by using the (B, C)-core inverse.

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