Let R be the set of nonnegative matrices whose row and column sums fall between specific limits and whose entries sum to some fixed h>0. Closely related axiomatic approaches have been developed to ascribe meanings to the statements: the real matrix f∈R and the integer matrix a∈R are ‘proportional to’ a given matrix p∈0. These approaches are described, conditions under which proportional solutions exist are characterized, and algorithms are given for finding proportional solutions in each case.
