Realizable lists on a class of nonnegative matrices

Abstract

A square matrix of order $n$ with $n\geq 2$ is called \textit{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.