The transformation of the states of polarization of electromagnetic waves through their interaction with polarimetrically linear media can be represented by the associated Mueller matrices. A global measure of the ability of a linear medium to modify the states of polarization of incident waves, due to any combination of enpolarizing, depolarizing and retarding properties, is introduced as the distance from the Mueller matrix to the identity matrix. This new descriptor, called the polarizing power, is applicable to any Mueller matrix and can be expressed as a function of the degree of polarimetric purity and the trace of the Mueller matrix. The graphical representation of the feasible values of the polarizing power provides a general view of its main peculiarities and features. The values of the polarizing power for several typical devices are analyzed.