The symmetric nonnegative inverse eigenvalue problem for 5 × 5 matrices Original Research Article

The symmetric nonnegative inverse eigenvalue problem (SNIEP) asks when a list σ=(λ1,λ2,…,λn) of n real numbers is the spectrum of an n×n symmetric nonnegative matrix. This problem is completely solved only for nless-than-or-equals, slant4. Our main goal here is to contribute to the solution of SNIEP for n=5. We also give a sufficient condition for a list σ to be realized as the spectrum of a symmetric positive matrix.