Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices
A Weyl type relative perturbation bound for the eigenvalues of \(A+E\) and \(A\), both positive definite, is extended to the indefinite Hermitian matrix case. This is applied to give a natural order perturbation bound for arbitrary Hermitian matrices \(A\) whose normal square root \(A^{1/2}\) satisfies \(\|A^{-1/2}EA^{-1/2}\|_2 \leq 1\) for the perturbation \(E\) that affects \(A\). Likewise there are applications to the variation of perturbed eigenspaces, perturbed singular values and singular vectors.
scientific article; zbMATH DE number 1443440
scientific article