  In applications of the density matrix renormalization group to nonhermitean
problems, the choice of the density matrix is not uniquely prescribed by the
algorithm. We demonstrate that for the recently introduced stochastic transfer
matrix DMRG (stochastic TMRG) the necessity to use open boundary conditions
makes asymmetrical reduced density matrices, as used for renormalization in
quantum TMRG, an inappropriate choice. An explicit construction of the largest
left and right eigenvectors of the full transfer matrix allows us to show why
symmetrical density matrices are the correct physical choice.
