Theoretical Properties of Biproportional Matrix Adjustments

The basic uniqueness and existence properties of biproportional matrix solutions are reviewed and a direct and constructive proof of the convergence of an iterative routine commonly adopted to adjust a given nonnegative matrix to produce a second matrix (biproportional to the first), whose row and column sums are given strictly positive numbers, is offered. Existing convergence proofs, most of which are limited to particular cases of the present form, are considered.