The NIEP is solvable by reality and finitely many polynomial inequalities
Algebraic Geometry
2024-07-22 v1
Abstract
The nonnegative inverse eigenvalue problem (NIEP) is shown to be solvable by the reality condition, spectrum equal to its conjugate, as well as by a finite union and intersection of polynomial inequalities. It is also shown that the symmetric NIEP and real NIEP form semi-algebraic sets and can therefore be solved just by a finite union and intersection of polynomial inequalities. An overview of ideas are given in how tools from real algebraic geometry may be applied to the NIEP and related sub-problems.
Keywords
Cite
@article{arxiv.2407.14472,
title = {The NIEP is solvable by reality and finitely many polynomial inequalities},
author = {Jared J. L. Brannan and Benjamin J. Clark},
journal= {arXiv preprint arXiv:2407.14472},
year = {2024}
}