Realizable lists on a class of nonnegative matrices

A square matrix of order n with n≥2 is called permutative matrix when all its rows are permutations of the first row. In this paper recalling spectral results for partitioned into 2-by-2 symmetric blocks matrices sufficient conditions on a given complex list to be the list of the eigenvalues of a nonnegative permutative matrix are given. In particular, we study NIEP and PNIEP when some complex elements in the lists under consideration have non-zero imaginary part. Realizability regions for nonnegative permutative matrices are obtained. A Guo's realizability-preserving perturbations result is obtained.