谱Perron多项式与Cauchy-Ostrovsky定理
Spectrally Perron Polynomials and the Cauchy-Ostrovsky Theorem
摘要：
本文简化了Cauchy和Ostrovsky定理的表述，并用组合非负矩阵理论给出了每个定理的证明。我们还表明，每个简单的充分条件在每个语句也是必要的，在其各自的情况下。此外，我们引入了光谱Perron多项式的概念，并提出了一个问题，呼吁广泛的数学观众。
英文摘要：
In this note, we simplify the statements of theorems attributed to Cauchy and Ostrovsky and give proofs of each theorem via combinatorial and nonnegative matrix theory. We also show that each simple sufficient condition in each statement is also necessary in its respective case. In addition, we introduce the notion of a spectrally Perron polynomial and pose a problem that appeals to a wide mathematical audience.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
