Preservation of stochasticity after perturbations

In order to result in a stochastic matrix A˜, the perturbation matrix E coming from the SCEPalgorithm should have positive matrix-elements corresponding to zero elements of the matrix A and should have negative elements corresponding to the 1 elements of A. In this working paper, we verify whether every stochastic 3 x 3 matrix can be perturbed such that the result is again a stochastic matrix. The focus is on the 0 and 1 elements in a stochastic 3 x 3 matrix. To end
up with a stochastic matrix A˜, the question is whether there exists a perturbation matrix E with perturbations on the zero elements of A that are positive, while the perturbations on the 1 elements of A are negative.