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On spectral variations under bounded real matrix perturbations. (English) Zbl 0747.65021

Given a matrix \(A\), the authors examine properties of the eigenvalue sets of perturbed matrices \(A+\Delta\), where \(\Delta\) is any matrix with \(\| \Delta\|\leq \rho\) for some given \(\rho\). They show that the spectral set (the set of numbers which are eigenvalues of \(A+\Delta\) for some \(\|\Delta\|\leq \rho\)) contains certain disks and intersections of disks about the eigenvalues of \(A\). The effect of similarity transformations on the behavior of the spectral set is examined.
Reviewer: S.Wright (Argonne)

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
15A42 Inequalities involving eigenvalues and eigenvectors
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References:

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