Rank equalities related to a class of outer generalized inverse | Zendy

Jianlong Chen | Zendy; Sanzhang Xu | Zendy; Julio Benítez | Zendy; Xiaofeng Chen | Zendy

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Rank equalities related to a class of outer generalized inverse

Author(s) -

Jianlong Chen,

Sanzhang Xu,

Julio Benítez,

Xiaofeng Chen

Publication year - 2019

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1917611c

Subject(s) - mathematics , rank (graph theory) , inverse , aka , drazin inverse , combinatorics , moore–penrose pseudoinverse , class (philosophy) , generalized inverse , ring (chemistry) , geometry , chemistry , organic chemistry , artificial intelligence , library science , computer science

In 2012, Drazin introduced a class of outer generalized inverse in a ring R, the (b,c)-inverse of a for a, b, c ? R and denoted by a||(b,c). In this paper, rank equalities of AkA||(B,C)- A||(B,C)Ak and (A*)kA||(B,C)-A||(B,C)(A*)k are obtained. As applications, weinvestigate equivalent conditions for the equalities (A*)kA||(B,C) = A||(B,C)(A*)k and AkA||(B,C) = A||(B,C)Ak. As corollaries we obtain rank equalities related to the Moore-Penrose inverse, the core inverse, and the Drazin inverse. The paper finishes with some rank equalities involving different e

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