  A proper set of indices characterizing the polarimetric purity of light and
material media is defined from the eigenvalues of the corresponding coherency
matrix. A simple and generalizable relation of these indices with the current
parameters characterizing the global purity is obtained. A general definition
for systems characterized by nxn positive semidefinite Hermitian matrices is
introduced in terms of the corresponding eigenvalues and diagonal Gell-Mann
matrices. The set of n-1 indices of purity has a nested structure and provide
complete information about the statistical purity of the system.
