On perturbations of non-diagonalizable stochastic matrices of order 3 (Q2288789)

Given a stochastic \(3\times 3\) matrix which is non-diagonalizable (hence has eigenvalues \(1\) and \(\lambda\)), it is proved that it is possible to perturb this matrix to obtain a new stochastic matrix whose eigenspace corresponding to the eigenvalue \(1\) is the same and with three different eigenvalues \(1\), \(\mu\), \(\nu\) such that \(\mu\), \(\nu\) are arbitrarily close to \(\lambda\).