A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES

摘要

＜正＞ In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of2×2 stochastic matrices are found explicitly.A method based on characteristic polynomial of matrix isdeveloped to find all real root matrices that are functions of the original 3×3 matrix, including allpossible（function）stochastic root matrices. In addition, we comment on some numerical methods forcomputing stochastic root matrices of stochastic matrices.