  We discuss a model of an X-ray illuminating source above an accretion disk of
a rotating black hole. Within the so called lamp-post scheme we compute the
expected (observed) polarization properties of the radiation reaching an
observer. We explore the dependencies on model parameters, employing Monte
Carlo radiation transfer computations of the X-ray reflection on the accretion
disk and taking general relativity effects into account. In particular, we
discuss the role of the black hole spin, of the observer viewing angle, and of
the primary X-ray source distance from the black hole. We give several examples
of the resulting polarization degree for two types of exemplary objects -
active galactic nuclei and Galactic black holes. In order to assess potential
observability of the polarization features, we assume the sensitivity of the
proposed New Hard X-ray Mission (NHXM).
  We examine the energy range from several keV to ~50 keV, so the iron-line
complex and the Compton hump are included in our model spectra. We find the
resultant polarization degree to increase at the higher end of the studied
energy band, i.e. at >~20 keV. Thus, the best results for polarimetry of
reflection spectra should be achieved at the Compton hump energy region. We
also obtain higher polarization degree for large spin values of the black hole,
small heights of the primary source, and low inclination angles of the
observer.
