ELA, Volume 16, pp. 1-18, January 2007, abstract.

Symmetric Nonnegative Realization of Spectra

Ricardo L. Soto, Oscar Rojo, Julio Moro, and Alberto Borobia

A perturbation result, due to R. Rado and presented by H. Perfect 
in 1955, shows how to modify r eigenvalues of a matrix of order n,
r<= n, via a perturbation of rank r, without changing any of
the n-r remaining eigenvalues. This result extended a previous
one, due to Brauer, on perturbations of rank r=1. Both results
have been exploited in connection with the nonnegative inverse
eigenvalue problem. In this paper a symmetric version of Rado's
extension is given, which allows us to obtain a new, more general,
sufficient condition for the existence of symmetric nonnegative
matrices with prescribed spectrum.