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A novel method for computing core-EP inverse through elementary transformation

  • Xingping Sheng EMAIL logo and Jinjin Mei
Published/Copyright: June 17, 2025

Abstract

Two novel representations of core-EP inverse A ( ) are derived for a deficient square matrix A C n × n with ind ( A ) = k . Based on the two representations, a new method to find the core-EP inverse A ( ) is presented through elementary transformation on a partitioned matrix. We summarize the corresponding algorithm for A ( ) and also analyze the computational complexities in detail. Our proposed algorithm is faster than that in [J. Ji and Y. Wei, The core-EP, weighted core-EP inverse of matrices and constrained systems of linear equations, Commun. Math. Res. 37 (2021), 1, 86–112] and [K. Manjunatha Prasad and M. D. Raj, Bordering method to compute core-EP inverse, Spec. Matrices 6 (2018), 193–200] by comparing their computational complexities under a certain condition. In the end, the efficiency of our algorithm is demonstrated by two numerical examples.

MSC 2020: 15A09; 65F05

Award Identifier / Grant number: 11901101

Award Identifier / Grant number: 1908085QA08

Award Identifier / Grant number: 2008085MA12

Funding statement: This project was supported by NSFC (11901101), NSF of Anhui Province (1908085QA08, 2008085MA12) and Top Talent in Subject (Specialty) Projects of Anhui Provincial University (gxbjZD2020072).

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Received: 2023-03-26
Revised: 2025-02-10
Accepted: 2025-05-28
Published Online: 2025-06-17
Published in Print: 2025-08-01

© 2025 Walter de Gruyter GmbH, Berlin/Boston

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