Eigenvalue perturbation

Summary

Eigenvalue perturbation studies how the eigenvalues and eigenvectors of a matrix change when the matrix is changed by a small amount. For a simple eigenvalue, the change is smooth, and its first-order term is given by left and right eigenvectors. Bounds such as Weyl's inequality and the Bauer–Fike theorem control the change without expansions. The subject matters for numerical computation, where matrices are known only up to rounding errors. It also matters in physics, where it is the base of perturbation theory.