Representations for the weak group inverse

作者：

Highlights：

• We propose new representations and characterizations of weak group inverse in terms of Moore-Penrose inverses or certain projections.

• We establish perturbation formulae for weak group inverse under some conditions.

• One splitting method for finding weak group inverse is studied.

• Successive matrix squaring (or SMS) algorithm for finding weak group inverse is given.

• Application of weak group inverse in solving some system of linear equations are presented too.

摘要

•We propose new representations and characterizations of weak group inverse in terms of Moore-Penrose inverses or certain projections.•We establish perturbation formulae for weak group inverse under some conditions.•One splitting method for finding weak group inverse is studied.•Successive matrix squaring (or SMS) algorithm for finding weak group inverse is given.•Application of weak group inverse in solving some system of linear equations are presented too.

论文关键词：Weak group inverse,Core-EP inverse,Perturbation

论文评审过程：Received 26 March 2020, Revised 28 November 2020, Accepted 3 January 2021, Available online 18 January 2021, Version of Record 18 January 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.125957