  The non-normality of Wilson-type lattice Dirac operators has important
consequences - the application of the usual concepts from the textbook
(hermitian) quantum mechanics should be reconsidered. This includes an
appropriate definition of observables and the refinement of computational
tools. We show that the truncated singular value expansion is the optimal
approximation to the inverse operator D^{-1} and we prove that due to the
gamma_5-hermiticity it is equivalent to gamma_5 times the truncated eigenmode
expansion of the hermitian Wilson-Dirac operator.
