PERTURBATION THEOREMS ON HERMITIAN MATRICES AND NEARLY HERMITIAN MATRICES

摘要

The problem of relating the eigenvalues of an n x n Hermitian matrix to those of its Rayleigh—Ritz approximation is considered. The same residual bound for unitarily invariant norms on Hermitian matrices is obtained even without the orlhonormal and Rayleigh—Ritz as- sumptions in Stewart and Sun's book [9, Theorem Ⅳ . 4.14]. The result can also be extended to nearly Hermitian matrices.