On the Partial Derivatives of Repeated Eigenvalues and their Eigenvectors

U Prells & MI Friswell (University of Wales Swansea)

AIAA Journal, Vol. 35, No. 8, August 1997, pp. 1363-1368

Abstract

The analysis of inverse problems in linear modelling often require the sensitivities of the eigenvalues and eigenvectors. The calculation of these sensitivities is mathematically related to the corresponding partial derivatives which do not exist for any parameterisation. Since eigenvalues and eigenvectors are coupled by the constitutional equation of the general eigenvalue problem their derivatives are coupled, too. In this paper conditions on the parameterisation are derived and formulated as theorems which ensure the existence of the partial derivatives of the eigenvalues and eigenvectors with respect to these parameters. The application of the theorems are demonstrated by examples.

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