Derivatives of complex eigenvectors with distinct and repeated eigenvalues

In this paper, we investigate the computation of the first-order derivatives of complex eigenvectors for general non-defective eigensystems. A new normalization condition is proposed, with which we can compute unique first-order derivatives of arbitrary differentiable eigenvectors of systems with distinct and repeated eigenvalues. We also present an efficient algorithm to compute the particular solutions to the governing equations of the first-order derivatives of eigenvectors. Finally, numerical examples are included to demonstrate the validity of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.

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