Given a non-negative real matrix $A \in R_+^{m \times n}$, how do i convert the matrix to doubly stochastic matrix i.e, each row summed to 1 and each column sums to one. In math terms,
Row Sum : $\sum_{j=1}^n A_{ij}= 1, \forall i= 1 \cdots m$
Column Sum : $\sum_{i=1}^m A_{ij}= 1, \forall j= 1 \cdots n$
Is the conversion is possible? if not, can we find a nearest matrix which is doubly stochastic matrix?