ELA, Volume 8, pp. 110-114, June 2001, abstract.

A Note on the Convexity of the Realizable Set of Eigenvalues for
Nonnegative Symmetric Matrices

C. Knudsen and J.J. McDonald

Geometric properties of the set Rn of n-tuples of realizable 
spectra of nonnegative symmetric matrices, and the Soules set 
Sn introduced by McDonald and Neumann, are examined.
It is established that S5 is properly contained in R5.
Two interesting examples are presented which show that neither  
Rn nor Sn need be convex. It is proved that Rn and Sn
are star convex and centered at (1,1,...,1).