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.

中文翻译：

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弱核逆的表达式及性质

本文开发了各种新的弱核逆及其对偶表达式。此外，还提出了弱核和双弱核逆的积分和极限表示以及微扰公式。我们研究了弱核逆及其对偶的连续性。考虑了上块三角矩阵的弱核和双弱核逆。给出了连续矩阵平方计算迭代方案的变体，用于计算弱核逆。