We report on directly determining the complex permittivity tensor using a method combining a developed light source from a segmented cross undulator of synchrotron radiation and the magneto-optical Kerr effect. The empirical permittivity, which carries the electronic and magnetic information of a material, has element specificity and has perfect confirmation using the quantum-mechanical calculation for itinerant electrons systems. These results help in understanding the interaction of light and matter, and they provide an interesting approach to seek the best materials as optical elements, for example, in extended-ultraviolet lithographic technologies or in state-of-the-art laser technologies.