Characterizations and representations for the m-core-EP inverse
Wu Hui, Huaquan Wei, Hongxing Wang, Hongwei Jin · Filomat · 2024
In this paper, we provide some characterizations and representations for the m-core-EP inverse. We give a relationship between the m-core-EP inverse and an invertible bordered matrix. Also, some charactizations for the m-core-EP inverse as an {2}-inverse with prescribed range and null space are presented. The Cramer?s rule for the solution of a singular equation Ax = b is also given. Perturbation bounds related with the m-core-EP inverse are estimated. Furthermore, the successive matrix squaring algorithm for com-puting the m-core-EP inverse is constructed. Finally, we show that the m-core-EP inverse can be used in solving appropriate systems of linear equations.