Chowdhry, G.Roy, F.2026-02-032025Indian Journal of Pure and Applied Mathematics, 2025, 56, 3, pp. 960-972195588https://doi.org/10.1007/s13226-025-00813-6https://idr.nitk.ac.in/handle/123456789/20100This 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 AT,S(2) is also obtained. Further, utilizing the full-rank decomposition of AT,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]. © The Indian National Science Academy 2025.Core-EP inverseGCEP inverseGeneralized inverseMoore-Penrose inverseOuter inverse