The current experimental data does not exclude the possibility that additional sterile neutrinos exist. We discuss two methods to determine active-sterile neutrino mixing. Firstly, singular values provide a comprehensive description of the mixing phenomena. By using them, we get the stringent bounds for the active-sterile mixing in the scenario with one additional neutrino. Secondly, we describe a simplified model with a sterile neutrino to show a sensitivity of the invisible Z-boson decay to the sterile neutrino mixings. In the end, we outline the precise analysis of the light-heavy mixings coming from the Z-boson decay taking into account the first-order radiative corrections.