On a realizable list by structured matrices spectrum

A square matrix of order n with $n \geq 2$ is called permutative matrix when all its rows (up to the frst one) are permutations of precisely its frst row. In this paper, the spectra of a class of permutative matrices are studied. In particular, spectral results for partitioned into 2 by 2 blocks doubly stochastic matrices are presented and, using these results sufcient conditions on a given list to be the list of eigenvalues of a nonnegative permutative matrix are obtained and the corresponding permutative matrices are constructed. Guo perturbations on given lists are exhibited.