The electro-optic polarization transmission characteristics of a liquid crystal (LC) cell is represented by a rotational transformation on the Poincare sphere, and its characteristic parameters, the angle and the axis of the rotation, are experimentally determined with respect to the voltage applied to the LC cell. From the experimental data obtained, we determine driving voltage for the LC cell to give the rotation angle near $180^{circ}$ of the rotation for the change of the state of the LC cell from non-select to select state, which is a necessary condition for the realization of maximally bright images. The directions of the transmission axes of the polarizer and the analyzer which form a liquid crystal display panel together with the LC cell, are determined from the general characteristics of the rotaional transformation of the LC cell. cell.