We introduce a 4×4 Mueller matrix for describing the polarization states of a liquid crystal cell. Using this Mueller matrix, it is possible to derive conditions whereby a linearly polarized input can be converted to either a perfectly linearly or perfectly circularly polarized output. These are called the perfect polarization conversion (PPC) conditions. These PPC conditions can be used in many different ways. For example, based on these PPC conditions, polarization mode switching schemes can be derived for the analysis of most liquid crystal displays.