5×5对称非负逆特征值问题的一个新不可能区域
A New Impossibility Region for the $5\times5$ Symmetric Nonnegative Inverse Eigenvalue Problem
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中文总结 AI 辅助
本文针对5×5对称非负逆特征值问题，提出新的低迹不可能区域，通过对角移位转化问题、简化互补交换矩阵为加权五元环，利用其特征多项式与谱恒等式推导矛盾，补充了该问题的理论边界。
中文摘要 AI 辅助
针对5×5对称非负逆特征值问题，我们提出了一个新的不可能区域，该区域位于低迹区域，据我们所知此前尚未被识别。证明过程采用合适的对角移位将问题转化为临界高迹边界，再将互补交换矩阵简化为加权五元环，该五元环的特征多项式与谱恒等式是推导矛盾的主要工具。
英文摘要
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.
