On nonnegative realization of partitioned spectra

We consider partitioned lists of real numbers � = {�1,�2,...,�n}, and give efficient and constructive sufficient conditions for the existence of nonnegative and symmetric nonnegative matrices with spectrum �. Our results extend the ones given in (R.L. Soto and O. Rojo. Applications of a Brauer theorem in the nonnegative inverse eigenvalue problem. Linear Algebra Appl., 416:844- 856, 2006.) and (R.L. Soto, O. Rojo, J. Moro, and A. Borobia. Symmetric nonnegative realization of spectra. Electron. J. Linear Algebra, 16:1-18, 2007.) for the real and symmetric nonnegative inverse eigenvalue problem. We also consider the complex case and show how to construct an r × r nonnegative matrix with prescribed complex eigenvalues and diagonal entries.