  This paper starts by deriving a factorization of the Loewner matrix pencil
that appears in the data-driven modeling approach known as the Loewner
framework and explores its consequences. The first is that the associated
quadruple constructed from the data yields a model without requiring further
processing. The second consequence is related to how sensitive the eigenvalues
of the Loewner pencil are to perturbations. Based on an explicit generalized
eigenvalue decomposition of this pencil and by making use of perturbation
theory of matrix pencils, we explore two types of eigenvalue sensitivities. The
first one is defined with respect to unstructured perturbations of the Loewner
pencil, while the second one is defined for structured perturbations. We also
discuss how the choice of data affects the two sensitivities.
