$M$-matrix, Group inverse, Proper splitting, Pseudo regular splitting, Weak pseudo regular splitting, $B_{\#}$-splitting.


In this article, generalizations of certain $M$-matrix properties are proved for the group generalized inverse. The proofs use the notion of proper splittings of one type or the other. In deriving certain results, we make use of a recently introduced notion of a $B_{\#}$-splitting. Applications in obtaining comparison results for the spectral radii of matrices are presented.

abs_vol31_pp686-705.pdf (25 kB)

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