Generalized core-EP inverse for square matrices

Sitha, B and Sahoo, JK and Behera, R and Stanimirovi�, PS and Stupina, AA (2023) Generalized core-EP inverse for square matrices. In: Computational and Applied Mathematics, 42 (8).

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Abstract

We introduce, investigate, and apply two types of generalized inverses for square complex matrices using an arbitrary inner inverse of the input matrix and its core-EP inverse. Introduced combinations of inner inverses and the core-EP inverse are termed inner core-EP (ICEP) and core-EP inner (CEPI) inverse. Additionally, we extend the notion of the P-core inverse for square matrices with arbitrary indices. A few equivalent characterizations and effective representations of the introduced generalized inverses are suggested. In addition, representations of these inverses are established via core-EP and HS decompositions. The induced binary relations for these inverses are introduced and their properties are considered. An application of the proposed inverses in solving linear systems is also discussed. © 2023, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.

Item Type:	Journal Article
Publication:	Computational and Applied Mathematics
Publisher:	Springer Nature
Additional Information:	The copyright for this article belongs to Springer Nature.
Keywords:	Inverse problems; Matrix algebra, Complex matrixes; Core-EP inverse; Drazin inverse; Generalized inverse; Inner inverse; Input matrix; Matrix partial orderings; Moore-Penrose inverse; Square complex; Square matrix, Linear systems
Department/Centre:	Division of Interdisciplinary Sciences > Computational and Data Sciences
Date Deposited:	28 Feb 2024 07:15
Last Modified:	28 Feb 2024 07:15
URI:	https://eprints.iisc.ac.in/id/eprint/83644

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