Semipositive matrices and their semipositive cones

The semipositive cone of A∈Rm×n,KA={x≥0:Ax≥0}, is considered mainly under the assumption that for some x∈ KA, Ax> 0 , namely, that A is a semipositive matrix. The duality of KA is studied and it is shown that KA is a proper polyhedral cone. The relation among semipositivity cones of two matrices is examined via generalized inverse positivity. Perturbations and intervals of semipositive matrices are discussed. Connections with certain matrix classes pertinent to linear complementarity theory are also studied.