Moore–Penrose inverse positivity of interval matrices

For A,B∈Rm×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.