论文标题
karpelevič地区重新审视
The Karpelevič Region Revisited
论文作者
论文摘要
我们考虑karpelevič区域$θ_n\ subset \ mathbb {c} $由订单$ n $的所有随机矩阵组成。我们提供了$θ_n$的替代表征，该表征削减了Karpelevič给出的原始描述。特别是，对于[0，2π）中的每个$θ\，我们确定了$θ_n$带有参数$θ的点上的点。
We consider the Karpelevič region $Θ_n \subset \mathbb{C}$ consisting of all eigenvalues of all stochastic matrices of order $n$. We provide an alternative characterisation of $Θ_n$ that sharpens the original description given by Karpelevič. In particular, for each $θ\in [0, 2π),$ we identify the point on the boundary of $Θ_n$ with argument $θ.$ We further prove that if $n \in \mathbb{N}$ with $n \ge 2,$ and $t \in Θ_n,$ then $t$ is a subdominant eigenvalue of some stochastic matrix of order $n$.
