Artikel,
On Differentiating Eigenvalues and Eigenvectors
Econometric Theory, 1 (2): pp. 179-191 (1985)
Zusammenfassung
Let X0 be a square matrix (complex or otherwise) and u0 a (normalized) eigenvector associated with an eigenvalue λ 0 of X0, so that the triple (X0,u0,λ 0) satisfies the equations Xu = λu, u0 * u=1. We investigate the conditions under which unique differentiable functions λ(X) and u(X) exist in a neighborhood of X0 satisfying λ (X0)=λ 0,u(X0)=Xu=λ u, and u0 * u=1. We obtain the first and second derivatives of λ(X) and the first derivative of u(X). Two alternative expressions for the first derivative of λ(X) are also presented.
