Nonnegative realization of complex spectra

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Ricardo L. Soto
Mario Salas
Cristina Manzaneda


We consider a list of complex numbers Λ = {λ1,λ2,.. .,λn} and give a simple and efficient sufficient condition for the existence of an n × n nonnegative matrix with spectrum Λ. Our result extends a previous one for a list of real numbers given in [Linear Algebra Appl., 416:844–856, 2006]. In particular, we show how to construct a nonnegative matrix with prescribed complex eigenvalues and diagonal entries. As a by-product, we also construct Hermitian matrices with prescribed spectrum, whose entries have nonnegative real parts.

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