A comprehensive physically realizable space, namely, the overall purity index-components of purity (PI4D-CP) space is proposed for the characterization of the depolarization caused by random (or deterministic) media. The overall purity index (PI4D)is obtained via indices of polarimetric purity which are incurred by the eigenvalues of the covariance matrix, whereas the components of purity (CP) are the functions of the elements of a Mueller matrix. On the one hand, the proposed space is useful in studying the depolarization caused by material media and on the other hand, it provides information on the diattenuation-polarizance properties of a Mueller matrix. Thus, it gives a remarkable physical insight of the depolarization problem.