The differences between the exact matrix of the Compton scattering and
the Rayleigh matrix of Thomson scattering have been investigated. We
present the Compton scattering formalism and, to illustrate this, comp
ute the polarization of radiation from a two-phase accretion disc as a
function of frequency and emission angle. The disc was assumed to be
plane parallel and consisting of two parts: 1. optically thick and coo
l inner disc emitting black body radiation and 2. hot optically thin a
ccretion disc corona (ADC). The central object was assumed not to cont
ribute to the X-ray luminosity and we neglected the radiation of the c
orona. The radiative transfer equation of polarized light was solved i
n the approximation of single scattering taking into account the exact
Compton matrix. It is shown that for high electron temperatures or fo
r large differences between the disc and coronal temperatures the Rayl
eigh matrix predicts much larger polarization values than the Compton
matrix.