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The 3-dimensional coherence matrix is interpreted by emphasising itsinvariance with respect to spatial rotations. Under these transformations, itnaturally decomposes into a real symmetric positive definite matrix,interpreted as the moment of inertia of the ensemble (and the correspondingellipsoid), and a real axial vector, corresponding to the mean angular momentumof the ensemble. This vector and tensor are related by several inequalities,and the interpretation is compared to those in which unitary invariants of thecoherence matrix are studied.Comment: 12 pages, 2 figures; revise

Geometric interpretation of the three-dimensional coherence matrix for nonparaxial polarization