Methods of Gauss–Jordan elimination to compute core inverse and dual core inverse
Xingping Sheng, Dawei Xin · Linear and Multilinear Algebra · 2020
In this paper, two formulas, which were studied by Wang and Liu (2015 Wang HX, Liu XJ. Characterizations of the core inverse and the core partial ordering. Linear Multilinear Algebra. 2015;63:1829–1836. doi: https://doi.org/10.1080/03081087.2014.975702[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Ma and Li (2019), respectively, for the core inverse, are simplified. Then two methods for computing the core inverse A◯# and dual core inverse A◯# are investigated through Gauss–Jordan elimination on the two appropriate block partitioned matrices. The corresponding algorithms are also summarized. The computational complexities of the these two algorithms are analysed in detail. In the end, some numerical examples are presented to demonstrate the efficiency of the two algorithms.