  An interval matrix is a matrix whose entries are intervals in the set of real
numbers. We generalize this concept, which has been broadly studied, to other
fields. Precisely we define a rational interval matrix to be a matrix whose
entries are intervals in the set of the rational numbers. We prove that a
(real) interval matrix with endpoints of all its entries in the set of the
rational numbers contains a rank-one matrix if and only if contains a rational
rank-one matrix and contains a matrix with rank smaller than min{p,q} if and
only if it contains a rational matrix with rank smaller than min{p,q}; from
these results and from the analogous criterions for (real) inerval matrices, we
deduce immediately a criterion to see when a rational interval matrix contains
a rank-one matrix and a criterion to see when it is full-rank, that is, all the
matrices it contains are full-rank. Moreover, given a field K and a matrix a
whose entries are subsets of K, we describe a criterion to find the maximal
rank of a matrix contained in a.
