On derivatives of eigenvalues, eigenvectors and generalized eigenvectors of matrices

Abstract

The classical linear eigenvalue problem is considered for matrices whose elements are dependent on a single real variable. Explicit expressions for derivatives of the eiegnvalues and eigenvectors are given in cases of simple and multiple eigenvalues. Recursion relations are obtained for derivatives of consecutively indexed generalized eigenvectors. Particular emphasis is placed on derivatives of eigenvectors and generalized eigenvectors to which enough coverage has not yet been provided in the present day literature.