On rank range of interval matrices

An interval matrix is a matrix whose entries are intervals in the set of the real numbers. Let p , q be nonzero natural numbers and let alpha=([\underline{alpha}_{i,j},overline{alpha}_{i,j}])_{i,j} be a p x q interval matrix; given a p x q matrix A with entries in R, we say that A is in alpha if a_{i,j} in [\underline{alpha}_{i,j}, overline{alpha}_{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 alpha with no more than 3 columns, we describe a way to find the range of the ranks of the matrices contained in alpha.