A generalization of Rohn's theorem on full-rank interval matrices
Elena Rubei · Linear and Multilinear Algebra · 2018
A general closed interval matrix is a matrix whose entries are closed connected nonempty subsets of R, while an interval matrix is defined to be a matrix whose entries are closed bounded nonempty intervals in R. We say that a matrix A with constant entries is contained in a general closed interval matrix μ if, for every i,j, we have that Ai,j∈μi,j. Rohn characterized full-rank square interval matrices, that is, square interval matrices μ such that every constant matrix contained in μ is nonsingular. In this paper, we generalize this result to general closed interval matrices.