In this paper we analyse the physical moaning of the eigenvalues and eigenvectors of the linear-transfomation and discuss the oscillation characteristics of the resonator, explain the differences and relationship among various types of the resonators and indicate that the variation from the Gaussian standing-wave resonator to the point-light-beam travelling-wave one is a radios change of the spotsize at the output mirror of the resonator from a finite value to an infinite one in substance. Finally the experimental results are compared with the above-mentioned theory.