Geodesic
New characterizations of weak group matrices
Filomat, Tome 37 (2023) no. 2, p. 457

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DOI

In this paper, we prove that a complex square matrix is weak group matrix if the m-th power of this matrix commutes with its weak group inverse, where m is an arbitrary positive integer. Firstly, some new characterizations of weak group matrices are investigated by means of core-EP decomposition. Secondly, we study new equivalent conditions of the weak group matrix by using commutator and rank equalities. Finally, the relationships between {m, k}-core EP matrices, k-EP matrices and weak group matrices are given.
DOI : 10.2298/FIL2302457Z
Classification : 15A09
Keywords: Weak group inverse, Weak group matrix, {m, k}-core EP matrix 
Mengmeng Zhou; Jianlong Chen; Néstor Thome. New characterizations of weak group matrices. Filomat, Tome 37 (2023) no. 2, p. 457 . doi: 10.2298/FIL2302457Z
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     author = {Mengmeng Zhou and Jianlong Chen and N\'estor Thome},
     title = {New characterizations of weak group matrices},
     journal = {Filomat},
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     year = {2023},
     volume = {37},
     number = {2},
     doi = {10.2298/FIL2302457Z},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2302457Z/}
}
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