Invariant indices of polarimetric purity

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 parameter characterizing the global purity is obtained. A general definition for systems characterized by n × n 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 provides complete information about the statistical purity of the system.