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 (1) spectrum of both the unperturbed and perturbed matrices, as well as, (2) spectrum of the unperturbed matrix only. The results presented give sightly 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不变化子空间的扰动的上限值,用量度值测量的矢量子空间面积为$\mathbb{C ⁇ n$,即(1)无扰动和扰动矩阵的频谱,以及(2)仅提供无扰动矩阵的频谱。结果比Davis-Khan $sin\sin\Theta$sortem 的定理线有近距离。我们将结果应用于图形扰动问题。