EIGENVALUE AND EIGENVECTOR DERIVATIVES OF A NONDEFECTIVE MATRIX

A novel approach is introduced to address the problem of the existence of differentiable eigenvectors for a nondefective matrix that may have repeated eigenvalues. The existence of eigenvector derivatives for a unique set of continuous eigenvectors corresponding to a repeated eigenvalue is rigorously established for nondefective and analytic matrices. A numerically implementable method is then developed to compute the differentiable eigenvectors associated with repeated eigenvalues. The solutions of eigenvalue and eigenvector derivatives for repeated eigenvalues are then derived. An example is given to illustrate the validity of formulations developed in this paper.