Sign pattern, usability, representations and perturbation for the core-EP and weighted core-EP inverse

Abstract

New properties and representations for the core-EP inverse are developed. Particularly, the core-EP inverse of an upper triangular matrix and its sign pattern are considered. Determinantal representations for the core-EP inverse and core-EP solution of linear systems are investigated. Corresponding representations of the weighted core-EP inverse are derived. The obtained results are illustrated by computational algorithms and illustrative examples. Certain results related to the perturbation constraints for the core-EP inverse are also provided. The results related with the core-EP inverse are a continuous of the results from [H. Ma and P.S. Stanimirović, Characterizations, approximation and perturbations of the Core-EP inverse, Appl. Math. Comput. 359 (2019), 404–417].