Resumen de Realizability by symmetric nonnegative matrices
Let Λ = {λ1, λ2,...,λn} be a set of complex numbers. The nonnegative inverse eigenvalue problem (NIEP) is the problem of determining necessary and sufficient conditions in order that Λ may be the spectrum of an entrywise nonnegative n × n matrix. If there exists a nonnegative matrix A with spectrum Λ we say that Λ is realized by A. If the matrix A must be symmetric we have the symmetric nonnegative inverse eigenvalue problem (SNIEP). This paper presents a simple realizability criterion by symmetric nonnegative matrices. The proof is constructive in the sense that one can explicitly construct symmetric nonnegative matrices realizing Λ.
