ELA, Volume 16, pp. 300-314, October 2007, abstract.

Computation of Eigenvalue and Eigenvector Derivatives 
for a General Complex-valued Eigensystem

N.P. van der Aa, H.G. ter Morsche, and R.M.M. Mattheij

In many engineering applications, the physical quantities that 
have to be computed are obtained by solving a related eigenvalue
problem. The matrix under consideration and thus its eigenvalues
usually depend on some parameters. A natural question then is how
sensitive the physical quantity is with respect to (some of) these
parameters, i.e., how it behaves for small changes in the
parameters. To find this sensitivity, eigenvalue and/or
eigenvector derivatives with respect to those parameters need to
be found. A method is provided to compute first order derivatives
of the eigenvalues and eigenvectors for a general complex-valued, 
non-defective matrix.