  A general analysis of the hydrodynamic limit of multi-relaxation time lattice
Boltzmann models is presented. We examine multi-relaxation time BGK collision
operators that are constructed similarly to those for the MRT case, however,
without explicitly moving into a moment space representation. The corresponding
'moments' are derived as left eigenvectors of said collision operator in
velocity space. Consequently we can, in a representation independent of the
chosen base velocity set, generate the conservation equations. We find a
significant degree of freedom in the choice of the collision matrix and the
associated basis which leaves the collision operator invariant. Therefore we
can explain why MRT implementations in the literature reproduce identical
hydrodynamics despite being based on different orthogonalization relations.
