A characterization of trace zero symmetric nonnegative 5x5 matrices

The problem of determining necessary and sufficient conditions for a set of real numbers to be the eigenvalues of a symmetric nonnegative matrix is called the symmetric nonnegative inverse eigenvalue problem (SNIEP). In this paper we solve SNIEP in the case of trace zero symmetric nonnegative 5x5 matrices.
Revised structure, fixed typos, added more details in some proofs, added figures