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Two generalized constrained inverses based on the core part of the Core-EP decomposition of a complex matrix

Xiaofei Cao^*, Sanzhang Xu, Xiaocai Wang, Kun Liu

 
ABSTRACT:     Let A be a complex matrix. The question when a generalized column constrained inverse coincides with a generalized row constrained inverse was answered, which lead to the generalized constrained inverse of A was introduced and this inverse coincides with the weak group inverse. Moreover, the ?distance? between the generalized constrained inverse and the inverse along two matrices was given, that is, the generalized constrained inverse of A coincides with the (A k ,(A k ) ?A)-inverse of A, where k is the index of A.

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* Corresponding author, E-mail: caoxiaofei258@126.com

Received 19 Dec 2022, Accepted 19 Jul 2023