Variational equations for the eigenvalues and eigenvectors of nonsymmetric matrices

The tracking of eigenvalues and eigenvectors for parameterized matrices is of major importance in optimization and stability problems. In the present paper, we consider a one-parameter family of matrices with distinct eigenvalues. A complete system of differential equations is developed for both the eigenvalues and the right and left eigenvectors. The computational feasibility of the differential system is demonstrated by means of a numerical example.The work of R. Kalaba and L. Tesfatsion was partially supported by the National Science Foundation under Grant No. ENG-77-28432 and by the National Institutes of Health under Grant No. GM-23732-03.