General expressions of propagation vector of electromagnetic wave for lossless anisotropic media

Three general representations of the eign-propagating vectors are presented for the lossless anisotropic medium, respectively. When the lossless medium is uniaxial crystal, the phase velocities and the corresponding eign-propagating vectors are entirely agreement with what in the literatures, when the medium is an isotropic one, the phase velocities and the corresponding eign-propagating vectors are also agreement with what in the literatures in theory. The validity of the results is demonstrated. The representations of these eign-propagating vectors are not confined by the permittivity tensor.