Generalized Core-EP Inverse: Representational and Computational Aspects

Geeta Chowdhry () and Falguni Roy ()
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Geeta Chowdhry: Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal
Falguni Roy: Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 960-972

Abstract: Abstract This study obtains several representations and properties of the generalized core-EP inverse (GCEP inverse). A novel canonical representation of the generalized core-EP inverse is obtained using the singular value decomposition (SVD). To accomplish this, a canonical representation of the $$A^{(2)}_{T,S}$$ A T , S ( 2 ) is also obtained. Further, utilizing the full-rank decomposition of $$A^{(2)}_{T,S}$$ A T , S ( 2 ) , some full-rank representations of the GCEP inverse are obtained, which in turn gives some new integral representations of the GCEP inverse. Additionally, algorithms and numerical examples are given using the representations obtained. Algorithms are implemented in Matlab R2024a, and it concluded that our algorithms are reliable and give more accurate results than the existing one in [1].

Keywords: Core-EP inverse; GCEP inverse; Outer inverse; Generalized inverse; Moore-Penrose inverse; 15A09; 15A23; 15A24 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00813-6

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