Eigenvalue perturbation
In mathematics, an eigenvalue perturbation problem is that of finding the eigenvectors and eigenvalues of a system A x = λ x {\displaystyle Ax=\lambda x} that is perturbed from one with known eigenvectors and eigenvalues A 0 x 0 = λ 0 x 0 {\displaystyle A_{0}x_{0}=\lambda _{0}x_{0}} . This is useful for studying how sensitive the original system's eigenvectors and eigenvalues x 0 i , λ 0 i , i = 1 , … n {\displaystyle x_{0i},\lambda _{0i},i=1,\dots n} are to changes in the system.