Individual Tracking of an Eigenvalue and Eigenvector of a Parameterized Matrix*

LET M(a) BE an n x n complex matrix-valued differentiable function of a parameter CI varying over some simply connected region Co of the complex plane C. In a previous paper [l] a complete initial value system of differential equations was developed for both the eigenvalues and right and left eigenvectors of M(a), assuming M(a) has IZ distinct eigenvalues for each c( in Co. In the present paper it is shown that an initial value system can also be developed for tracking a single eigenvalue of M(a) together with one of its corresponding right or left eigenvectors. The computational feasibility of the initial value system is illustrated by numerical example.