Relative residual bounds for indefinite Hermitian matrices

We prove several residual bounds for relative perturbations of the eigenvalues of indefinite Hermitian matrix. The bounds fall into two categories––the Weyl-type bounds and the Hofmann–Wielandt-type bounds. The bounds are expressed in terms of sines of acute principal angles between certain subspaces associated with the indefinite decomposition of the given matrix. The bounds are never worse than the classical residual bounds and can be much sharper in some cases. The bounds generalize the existing relative residual bounds for positive definite matrices to indefinite case.