The nonnegative inverse eigenvalue problem (NIEP) asks for necessary and
sufficient conditions for the existence of a nonnegative matrix with
prescribed eigenvalues. In this work, we consider two topics of the problem:
First, by introducing a particular partition, we improve previous sufficient
conditions for both, the real and symmetric cases. Second, we prove a Guo
type perturbation result for the imaginary parts of complex eigenvalues,
while keeping nonnegativity.
