Despite the intrinsic coupling between electric and magnetic fields in random stationary light, their polarization properties are not mutually determined. A complete second-order description thus necessitates a joint electromagnetic treatment. The $6\times 6$ electromagnetic polarization matrix introduced here generalizes the conventional electric $3\times 3$ matrix by incorporating both electric and magnetic contributions together with their mutual correlations. It consists of diagonal $3\times 3$ blocks, representing the electric and magnetic polarization matrices, and off-diagonal $3\times 3$ blocks that encode the full structure of electric-magnetic cross correlations. The information contained in this matrix can be interpreted through physically meaningful quantities such as active and reactive energy fluxes, in-phase and quadrature alignment matrices, and global indices describing electric-magnetic coupling. The formalism is applied to a field composed of two orthogonally propagating plane waves sharing a common linear electric polarization (a simple yet physically realizable configuration) that demonstrates the need for a general combined electric-magnetic representation even in free space. This approach provides a comprehensive and unified framework for characterizing electromagnetic polarization beyond the electric-field description alone, bridging classical statistical optics with quantumlike density-matrix interpretations.

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• Polarization of light