  It has been observed that the reduced density matrices of bipartite qudit
pure states possess a Gram matrix structure. This observation has opened a
possibility of analysing the entanglement in such systems from the purely
geometrical point of view. In particular, a new quantitative measure of an
entanglement of the geometrical nature, has been proposed. Using the invented
Gram matrix approach, a version of a non-linear purification of mixed states
describing the system analysed has been presented.
