Invariant indices of polarimetric purity Generalized indices of purity for n x n covariance matrices

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 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 provides complete information about the statistical purity of the system. (C) 2010 Elsevier B.V. All rights reserved.