On symmetric nonnegative matrices with prescribed spectrum

Abstract

In this paper we give a sufficient condition for the existence and construction of a symmetric nonnegative matrix with prescribed spectrum, and a sufficient conditon for the existence and construction of a 4 × 4 symmetric nonnegative matrix with prescribed spectrum and diagonal entries. This last condition is independent of the sufficient condition given by Fiedler [LAA 9 (1974) 119-142]. We also give some partial answers on an open question of Guo [LAA 266 (1997)