A note on eigenvalues of perturbed Hermitian matrices Original Research Article

Letimage be Hermitian matrices with eigenvalues λ1 greater-or-equal, slanted cdots, three dots, centered greater-or-equal, slanted λk and image, respectively. Denote by short parallelEshort parallel the spectral norm of the matrix E, and η the spectral gap between the spectra of H1 and H2. It is shown thatimage which improves all the existing results. Similar bounds are obtained for singular values of matrices under block perturbations.