Basic properties and classification of Mueller matrices derived from their statistical definition

Starting from the statistical definition of the Mueller matrix, we derive the relationships between basic properties, such as the number of contact points of the characteristic ellipsoid with the Poincaré sphere and the rank of the covariance matrix. This approach enables the comprehensive classification of any experimental depolarizing Mueller matrix into one of six possible classes, thus making possible phenomenological interpretation in terms of a specific fluctuating Jones generator or of a finite sum of nondepolarizing Mueller matrices.