The classical Davis-Kahan theorem provides an efficient bound on the perturbation of eigenspaces of a matrix under a large (eigenvalue) gap condition. In this paper, we consider the case when the gap is moderate. Using a bootstrapping argument, we obtain a new bound which is efficient when the perturbation matrix is uncorrelated to the ground matrix. We believe that this bound is sharp up to a logarithmic term.

翻译：经典的戴维斯-卡汉定理在（特征值）大间隙条件下给出了矩阵特征空间扰动的高效界。本文研究间隙为中等程度的情形。通过自助法论证，我们得到了一个当扰动矩阵与基础矩阵不相关时仍然高效的新界。我们相信该界除对数项外是尖锐的。