  ADER-WENO methods have proved extremely useful in obtaining arbitrarily
high-order solutions to problems involving hyperbolic systems of PDEs. For
example, it has been demonstrated that for the same computational cost as a
Runge-Kutta scheme of a certain order, one can obtain an ADER scheme of one
higher order of accuracy. Additionally, Runge-Kutta schemes suffer from the
presence of Butcher barriers, limiting the order of temporal accuracy that one
can comfortably achieve. There are no such limitations present in ADER-WENO
schemes.
  The cumbersome analytical derivation of the temporal derivatives of the
solution required by the original ADER formulation has been replaced by the use
of a cell-wise local Galerkin predictor. The predictor can take either a
discontinuous or a continuous form. The Galerkin predictor is a high-order
polynomial reconstruction of the data in both space and time, found as the root
of a non-linear system.
  It has been conjectured that the eigenvalues of certain matrices appearing in
these non-linear systems are always zero, leading to desirable system
properties for certain classes of PDEs. It is proved here that this is in deed
the case for any number of spatial dimensions and any desired order of
accuracy, for both the discontinuous and continuous Galerkin variants. This
result is independent of the choice of reconstruction basis polynomials.
