We provide upper bounds on the perturbation of invariant subspaces of normal matrices measured using a metric on the space of vector subspaces of $\mathbb{C}^n$ in terms of the spectrum of both the unperturbed \& perturbed matrices, as well as, spectrum of the unperturbed matrix only. The results presented give tighter bounds than the Davis-Khan $\sin\Theta$ theorem. We apply the result to a graph perturbation problem.

翻译：我们提供正常矩阵的无变子空间扰动的上限值,用量度值测量的矢量子空间空间面积为$\mathbb{C ⁇ n$的值来测量正常矩阵的无变子空间,其范围包括无扰动的 ⁇ 扰动矩阵的频谱,以及只有未扰动的矩阵的频谱。结果比 Davis-Khan $sin\sin\Theta$sultem 的值更严格。我们将结果应用于图表扰动问题 。