  We study geometrical aspects of entanglement, with the Hilbert--Schmidt norm
defining the metric on the set of density matrices. We focus first on the
simplest case of two two-level systems and show that a ``relativistic''
formulation leads to a complete analysis of the question of separability. Our
approach is based on Schmidt decomposition of density matrices for a composite
system and non-unitary transformations to a standard form. The positivity of
the density matrices is crucial for the method to work. A similar approach
works to some extent in higher dimensions, but is a less powerful tool. We
further present a numerical method for examining separability, and illustrate
the method by a numerical study of bound entanglement in a composite system of
two three-level systems.
