We investigated the light reflection from half-space of cholesteric liquid crystal (CLC) being in external static magnetic field directed along the helix axis at normal light incidence. In this case there appear three photonic band gaps (PBGs) and these bands can be tuned in large intervals. We found the eigenpolarizations (EPs) at reflection of light from half-space and investigated their peculiarities. We have shown that in the absence both of absorption and of external magnetic field and at minimal influence of dielectric boundary (when the dielectric permittivity of isotropic half-space which borders with CLC half-space is equal to the CLC's mean dielectric permittivity) these polarizations are orthogonal. While, in the presence of external magnetic field they become quasi-orthogonal everywhere outside the main PBG (which exist also at the absence of external magnetic field), and they are significantly non-orthogonal within the main PBG. At some values of helix pitch they become significantly non-orthogonal practically everywhere. Moreover, in this case there exist some special points where the EPs degenerate. This system can apply as tunable narrow-band or broad-band filter and mirror, a highly tunable broad/narrow-band optical diode, and other devices.