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On a perturbation bound for invariant subspaces of matrices

Karow, Michael; Kressner, Daniel

FG Numerische Lineare Algebra

Given a nonsymmetric matrix A, we investigate the effect of perturbations on an invariant subspace of A. The result derived in this paper differs from Stewart's classical result and sometimes yields tighter bounds. Moreover, we provide norm estimates for the remainder terms in well-known perturbation expansions for invariant subspaces, eigenvectors, and eigenvalues.