  We present three different matrix bases that can be used to decompose density
matrices of d--dimensional quantum systems, so-called qudits: the generalized
Gell-Mann matrix basis, the polarization operator basis, and the Weyl operator
basis. Such a decomposition can be identified with a vector --the Bloch vector,
i.e. a generalization of the well known qubit case-- and is a convenient
expression for comparison with measurable quantities and for explicit
calculations avoiding the handling of large matrices. We consider the important
case of an isotropic two--qudit state and decompose it according to each basis.
Investigating the geometry of entanglement of special parameterized two--qubit
and two--qutrit states, in particular we calculate the Hilbert--Schmidt measure
of entanglement, we find that the Weyl operator basis is the optimal choice
since it is closely connected to the entanglement of the considered states.
