Moore–Penrose inverse positivity of interval matrices

Abstract

For A , B ∈ R m × n , let J = [ A , B ] be the set of all matrices C such that A ≤ C ≤ B , where the order is component wise. Krasnosel’skij et al. [9] and Rohn [11] have shown that if A and B are invertible with A - 1 ≥ 0 and B - 1 ≥ 0 , then every C ∈ J is invertible with C - 1 ≥ 0 . In this article, we present certain extensions of this result to the singular case, where the nonnegativity of the usual inverses is replaced by the nonnegativity of the Moore–Penrose inverse.