A generalization of Rohn's theorem on full-rank interval matrices

Abstract

A general closed interval matrix is a matrix whose entries are closed connected nonempty subsets of the set of the real numbers, while an interval matrix is defined to be a matrix whose entries are closed bounded nonempty intervals in the set of real numbers. We say that a matrix $A$ with constant entries is contained in a general closed interval matrix $\mu$ if and only if, for every $i,j$, we have that $A_{i,j} \in \mu_{i,j}$. Rhon characterized full-rank square interval matrices, that is, square interval matrices $\mu$ such that every constant matrix contained in $\mu$ is nonsingular. In this paper we generalize this result to general closed interval matrices.