  A hyperbolic system must have a set of linearly independent eigenvectors and
corresponding real eigenvalues. In numerical simulations, however, the
eigenvalues can be complex because truncation errors pollute a characteristic
polynomial of the hyperbolic system. Here we propose an
eigenstructure-preserving scheme which always generates the real eigenvalues,
even in discrete level. Although the eigenstructure is discussed in a
non-conservative formulation, the proposed scheme is locally conservative owing
to the skew-symmetric operators.
