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arXiv · 2608.19435

A New Impossibility Region for the $5\times5$ Symmetric Nonnegative Inverse Eigenvalue Problem

Jiashun Jin·Zheng Tracy Ke·Bingcheng Sui
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Abstract

We present a new impossibility region for the $5\times5$ symmetric nonnegative inverse eigenvalue problem. The region lies in the low-trace regime and, to the best of our knowledge, has not been identified previously. The proof uses a suitable diagonal shift to transform the problem to a critical high-trace boundary and then reduces a complementary commuting matrix to a weighted five-cycle. The characteristic polynomial and spectral identities of this five-cycle provide the main tools for deriving the resulting contradiction.

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Jiashun Jin, Zheng Tracy Ke, Bingcheng Sui. 2026-08-19. A New Impossibility Region for the $5\times5$ Symmetric Nonnegative Inverse Eigenvalue Problem. https://arxiv.org/abs/2608.19435

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