ABSTRACT
In this paper, we present necessary and sufficient conditions for the k-commutative equality , where X is an outer generalized inverse of the square matrix A. Also, we give new representations for core EP, DMP, and CMP inverses of square matrices as outer inverses with prescribed null space and range. In addition, we characterize the core EP inverse as the solution of a new system of matrix equations.
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Acknowledgements
The authors would like to thank the referees for their valuable comments which helped to improve the readability of the manuscript.
Disclosure statement
No potential conflict of interest was reported by the authors.