Jeyaraman, I.Sivakumar, K.C.2026-02-052016Linear Algebra and Its Applications, 2016, 510, , pp. 42-63243795https://doi.org/10.1016/j.laa.2016.08.003https://idr.nitk.ac.in/handle/123456789/25865For a matrix A whose off-diagonal entries are nonpositive, its nonnegative invertibility (namely, that A is an invertible M-matrix) is equivalent to A being a P-matrix, which is necessary and sufficient for the unique solvability of the linear complementarity problem defined by A. This, in turn, is equivalent to the statement that A is strictly semimonotone. In this paper, an analogue of this result is proved for singular symmetric Z-matrices. This is achieved by replacing the inverse of A by the group generalized inverse and by introducing the matrix classes of strictly range semimonotonicity and range column sufficiency. A recently proposed idea of P<inf>#</inf>-matrices plays a pivotal role. Some interconnections between these matrix classes are also obtained. © 2016 Elsevier Inc.Matrix algebraGroup inverseLinear complementarity problemsM-matricesMonotonicityRange column sufficiencyStrictly range semimonotonicityInverse problems