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arXiv · 2407.14472

The NIEP is solvable by reality and finitely many polynomial inequalities

Jared J. L. Brannan·Benjamin J. Clark
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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.

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Jared J. L. Brannan, Benjamin J. Clark. 2024-07-19. The NIEP is solvable by reality and finitely many polynomial inequalities. https://arxiv.org/abs/2407.14472

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