We extend several relative perturbation bounds to Hermitian matrices that are possibly singular, and also develop a general class of relative bounds for Hermitian matrices. As a result, corresponding relative bounds for singular values of rank-deficient $m\times n$ matrices are also obtained using the Jordan-Wielandt matrices. We also present that the main relative bound derived would be invariant with respect to congruence transformation under certain conditions, and compare its sharpness with the Weyl's absolute perturbation bound.

翻译：我们将若干相对扰动界推广至可能奇异的Hermitian矩阵，并发展了一类适用于Hermitian矩阵的通用相对扰动界。由此，通过Jordan-Wielandt矩阵，我们还得到了秩亏缺$m\times n$矩阵的奇异值的相应相对扰动界。此外，我们证明了所导出的主相对扰动界在特定条件下关于合同变换具有不变性，并将其紧致性与Weyl绝对扰动界进行了比较。