Inverse elementary divisor problem for nonnegative matrices
Henryk Minc · Proceedings of the American Mathematical Society · 1981
Given a diagonalizable positive matrix A A , there exists a positive matrix with the same spectrum as A A , and with arbitrarily prescribed elementary divisors, provided that elementary divisors corresponding to nonreal eigenvalues occur in conjugate pairs. It is also shown that a similar result holds for doubly stochastic matrices.