Partial dertivatives of repeated eigenvalues and their eigenvectors

摘要

The analysis of inverse problems in linear modeling often require the sensitivities of the eigenvalues and eigenvec- tors. The calculation of these sensitivitis is mathematically related to the corresponding partial derivatives, which do not exist for any parameterization. Inasmuch as eigenvalues and eigenevectors re coupled by the constitutional equation of he general eigenvalue problem, their derivatives are coupled, too.