  The method of characteristics is a classical method for gaining understanding
in the solution of a partial differential equation. It has recently been
applied to the adjoint equations of the 2D Euler equations and the first goal
of this paper is to present a linear algebra analysis that greatly simplifies
the discussion of the number of independant characteristic equations satisfied
along a family of characteristic curves. This method may be applied for both
the direct and the adjoint problem and our second goal is to directly derive in
conservative variables the characteristic equations of 2D compressible inviscid
flows. Finally, the theoretical results are assessed for a nozzle flow with a
classical scheme and its dual consistent discrete adjoint.
