Weak monotonicity of A versus {1}-inverses nonnegative on the range space of A

This short note presents a sufficient condition under which a question raised by Peris and Subiza, namely, to find a {1}-inverse X ∈ Rn × m of a matrix A ∈ Rm × n such that A is weak monotone if and only if X is nonnegative on R (A), is answered in the affirmative. © 2007 Elsevier Inc. All rights reserved.