where the state vector
and the flux vector
are defined in (6) and (7), respectively. In the following we explicitly give both the
eigenvalues and the right and left eigenvectors of the Jacobi
matrix
only (the cases
*i*
=
*y*,
*z*
are easily obtained by symmetry considerations).

The eigenvalues of matrix are

and

A complete set of right-eigenvectors is

where

The corresponding complete set of left-eigenvectors is

where is the determinant of the matrix of right-eigenvectors, i.e.,

For an ideal gas equation of state , i.e., , and hence for .

Numerical Hydrodynamics in Special Relativity
Jose Maria Martí and Ewald Müller
http://www.livingreviews.org/lrr-1999-3
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