On rank range of interval matrices

An interval matrix is a matrix whose entries are intervals in R. Let p,q∈N∖{0} and let α=([α_i,j,α‾i,j])i,j be a p×q interval matrix; given a p×q matrix A with entries in R, we say that A∈α if ai,j∈[α_i,j,α‾i,j] for any i,j. We establish a criterion to say if an interval matrix contains a matrix of rank 1. Moreover we determine the maximum rank of the matrices contained in a given interval matrix. Finally, for any interval matrix α with no more than 3 columns, we describe a way to find the range of the ranks of the matrices contained in α.