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.
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