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Nonlocal sensitivity analysis of the eigensystem of a matrix with distinct eigenvalues

New nonlocal nonlinear perturbation bounds are derived for the eigensystem (eigenvectors and eigenvalues) of an n x n matrix with pair-wise distinct eigenvalues. The construction of the perturbation bounds re-quires the solution of an n-degree algebraic equation. To avoid this, asymptotic expansions and other approximations to the perturbation bounds are proposed as well. The case n = 2 is considered in detail and it is shown that for a class of perturbations the proposed bounds are relatively sharp.A comparison is made with the known nonlocal perturbation results for the Schur system of a matrix.