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Polarization could be the last resource to be exploited for space-limited devices. Over the past years, theoretical studies and experimental work present different conclusions on the potential increase in the number of degrees of freedom from polarization. This paper attempts to unify the different conclusions and provide a mathematical framework that can be applied to any array geometry and channel scattering condition. It shows that the degree-of-freedom gain from using polarimetric antenna elements ranges from 2 to 6 and the gain depends on the array geometry and the channel scattering condition. Sampling techniques and vector multipole decomposition are applied to derive the results.