Classification of singular points in polarization field of CMB and eigenvectors of Stokes matrix

Analysis of the singularities of the polarization field of CMB, where polarization is equal to zero, is presented. It is found that the classification of the singular points differs from the usual three types known in the ordinary differential equations. The new statistical properties of polarization field are discussed, and new methods to detect the presence of primordial tensor perturbations are indicated.