A novel method for computing core-EP inverse through elementary transformation
Xingping Sheng, Jin-Jin Mei · Journal of Inverse and Ill-Posed Problems · 2025
Abstract Two novel representations of core-EP inverse A ( † ) A^{({\dagger})} are derived for a deficient square matrix A ∈ C n × n A\in C^{n\times n} with ind ( A ) = k \operatorname{ind}(A)=k . Based on the two representations, a new method to find the core-EP inverse A ( † ) A^{({\dagger})} is presented through elementary transformation on a partitioned matrix. We summarize the corresponding algorithm for A ( † ) A^{({\dagger})} 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.