发表机构
Isfahan University of Technology; University of Regina（伊斯法罕理工大学; 里贾纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究热带全非负矩阵的经典与热带特征值赋值相等的条件，指出主导消去是唯一障碍，并给出基于牛顿多边形断点一致性的充要判据及例外提升的显式方程。
AI 中文摘要
设 $\mathbf A$ 是实数闭非阿基米德赋值域上的全非负矩阵，并假设其赋值 $A$ 是热带全非负的。尽管经典特征值的赋值被 $A$ 的热带特征值弱优超，但等式可能因消去而失效。我们给出了等式成立的充分必要条件。唯一的障碍是主余子式中的主导消去，这些主余子式给出了热带特征多项式的基本系数。换言之，当且仅当经典与热带牛顿多边形在对角线元素所确定的断点处一致时，等式成立。我们通过首项系数的显式多项式方程来描述例外提升。我们还在可允许参数空间的每个不可约分量上研究这些方程。最后，我们给出了完整的 $3\times 3$ 判据，并构造了一个包含具有谱等式的普通提升和不具有谱等式的例外全非负提升的族。
英文摘要
Let $\mathbf A$ be a totally nonnegative matrix over a real closed non-Archimedean valued field, and suppose that its valuation $A$ is tropically totally nonnegative. Although the valuations of the classical eigenvalues are weakly majorized by the tropical eigenvalues of $A$, equality can fail through cancellation. We give a necessary and sufficient condition for equality. The only obstruction is dominant cancellation in the principal minors that give the essential coefficients of the tropical characteristic polynomial. In other words, equality holds exactly when the classical and tropical Newton polygons agree at the breakpoints determined by the diagonal entries. We describe the exceptional lifts by explicit polynomial equations in the leading coefficients. We also study these equations on each irreducible component of the admissible parameter space. Finally, we give a complete $3\times 3$ criterion and a family that contains both ordinary lifts with spectral equality and exceptional totally nonnegative lifts without it.
Comments19 pages
