Closest matrices in the space of generalized doubly stochastic matrices

Let <(Omega)over cap>(n) denote the set of generalized doubly stochastic n x n real matrices; that is matrices whose row and column sums are 1. The research in this paper concerns finding the closest matrix B* in <(Omega)over cap>(n) to a given matrix A in M-n, the space of n x n real matrices. Let J(n) be the n x n matrix whose entries are all equal to 1/n and let I-n be the n x n identity matrix in M-n. We prove that B* = WAW + J(n), where W = I-n - J(n). (C) 1998 Academic Press.