Nondepolarizing Mueller matrices contain up to seven independent parameters. However, these seven parameters typically do not appear explicitly among the measured 16 parameters of a Mueller matrix, so that they are not directly accessible for physical interpretation. This work shows that all the information contained in a nondepolarizing Mueller matrix can be conveniently expressed in terms of a four component covariance vector state or a generating matrix, which can be understood as a matrix state. The generating matrix, besides being directly related to the nondepolarizing Mueller matrix, mimics all properties of the Jones matrix and provides a powerful mathematical tool for formulating all properties of nondepolarizing systems, including the Mueller symmetries and the anisotropy coefficients.
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