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In this paper, two formulas, which were studied by Wang and Liu ( 2015 ) and Ma and Li (2019), respectively, for the core inverse, are simplified. Then two methods for computing the core inverseand dual core inverseare 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.

Methods of Gauss–Jordan elimination to compute core inverse and dual core inverse