Jordan矩阵的扰动
Perturbations of Jordan Matrices
摘要：
我们考虑扰动的一个大的约旦矩阵，随机和小的范数或小秩。在这两种情况下，我们表明，大多数的扰动矩阵的特征值是非常接近一个圆的中心在原点。在随机扰动的情况下，我们获得了在某种渐进状态下完全位于圆内的特征值数量的估计。在有限秩扰动的情况下，我们完全确定谱渐近矩阵的大小增加。本文对谱理论的一些标准方法作了初步的说明。
英文摘要：
We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In both cases we show that most of the eigenvalues of the perturbed matrix are very close to a circle with centre at the origin. In the case of random perturbations we obtain an estimate of the number of eigenvalues that are well inside the circle in a certain asymptotic regime. In the case of finite rank perturbations we completely determine the spectral asymptotics as the size of the matrix increases. The paper provides an elementary illustration of some standard techniques of spectral theory.
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