Variational Equations for the Eigenvalues and Eigenvectors of Nonsymmetric Matrices

This article develops a complete system of ordinary differential equations for tracking the eigenvalues and the right and left eigenvectors of nonsymmetric parameterized matrices over parameter intervals. A simpler reduced form of the ODE system is then derived for tracking the eigenvalues and eigenvectors of symmetric parameterized matrices. The feasibility and accuracy of the tracking method are illustrated by numerical examples. Annotated pointers to related work can be accessed here: http://www.econ.iastate.edu/tesfatsi/nasahome.htm