Stability of Eigenvalues and Spectral Decompositions Under Linear Perturbation

Abstract Given an n-by-n matrix A and a fixed perturbation matrix E, the effect of the linear perturbations A+tE, t∈ C , on certain spectral properties of A is analyzed. Specially the effect of the structure of E on these properties is investigated. A geometric framework for spectral analysis of A+tE is developed to achieve this goal which also leads to a better understanding of the sensitivity of eigenvalues and spectral decompositions of A.

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