Expressions and properties of weak core inverse

摘要

Various novel expressions of weak core inverse and its dual are developed in this paper. In addition, integral and limit representations as well as perturbation formulae for the weak core and dual weak core inverses are presented. We investigate continuity for the weak core inverse and its dual. The weak core and dual weak core inverses for upper block triangular matrix are considered. A variant of the successive matrix squaring computational iterative scheme is given for calculating the weak core inverse.