Closest matrices in the space of generalized doubly stochastic matrices (Q1270897)

The author constructs the closest matrix \(B^*\) in \(\Omega_n\) (the collection of doubly stochastic \(n\times n\) real matrices) to a given real matrix \(A\) in \(M_n\) (the space of all \(n\times n\) real matrices). He also proves that \(B^* =(I_n-J_n) A(J_n-J_n) +J_n\), where \(J_n\) is \(n\times n\) real matrix the entries of which are all equal to \(1/n\) and \(I_n\) is \(n\times n\) real identity matrix in \(M_n\).