An experimental approach to the NIEP using algebraic geometry
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Abstract: The nonnegative inverse eigenvalue problem (NIEP) asks for the necessary and sufficient conditions for a list of complex numbers to be the spectra of a nonnegative matrix. Using tools from algebraic geometry, it is shown that the NIEP is solvable by polynomial inequalities and the reality condition. An experimental approach is then presented for forming the desired feasibility region of the NIEP for small matrices. We conclude by proving that under this approach, solving the real NIEP solves the NIEP.