The analysis of inverse problems in linear modeling often require the
sensitivities of the eigenvalues and eigenvectors, The calculation of
these sensitivities is mathematically related to the corresponding par
tial derivatives, which do not exist for any parameterization, Inasmuc
h as eigenvalues and eigenvectors are coupled by the constitutional eq
uation of the general eigenvalue problem, their derivatives are couple
d, too, Conditions on the parameterization 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 is demonstrated by examples.