New multiplicative perturbation bounds for orthogonal projection in a general unitarily invariant norm, the Q-norm and the spectral norm are derived. These bounds always improve the existing bounds. An example is given to show that these new bounds are optimal.

中文翻译：

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正交投影的新乘法扰动界

推导了广义酉不变范数、Q范数和谱范数中正交投影的新乘法扰动界。这些边界总是改进现有的边界。给出了一个例子来说明这些新的界限是最优的。