The significance of eigenvectors and eigenvalues of Lorentz transformation matrix in the process of diagonalization are discussed. The procedure of diagonalizing Lorentz transformation matrix is to transform the general inertial frame of reference into the light-cone coordinate system. The eigenvectors are the vectors on the axis of light-cone coordinate system. The eigenvalues correspond to the scaling factor for the light-cone coordinate components under the reference frame transformation. This paper can help students to deepen their understanding of Lorentz transformation and the space-time characteristics of special relativity.