  Singular values are used to construct physically admissible 3-dimensional
mixing matrices characterized as contractions. Depending on the number of
singular values strictly less than one, the space of the 3-dimensional mixing
matrices can be split into four disjoint subsets, which accordingly corresponds
to the minimal number of additional, non-standard neutrinos. We show in
numerical analysis that taking into account present experimental precision and
fits to different neutrino mass splitting schemes, it is not possible to
distinguish, on the level of 3-dimensional mixing matrices, between two and
three extra neutrino states. It means that in 3+2 and 3+3 neutrino mixing
scenarios, using the so-called $\alpha$ parametrization, ranges of non-unitary
mixings are the same. However, on the level of a complete unitary 3+1 neutrino
mixing matrix, using the dilation procedure and the Cosine-Sine decomposition,
we were able to shrink bounds for the "light-heavy" mixing matrix elements. For
instance, in the so-called seesaw mass scheme, a new upper limit on $| U_{e4} |
$ is about two times stringent than before and equals 0.021. For all considered
mass schemes the lowest bounds are also obtained for all mixings, i.e. $|
U_{e4} | , | U_{\mu 4} | , | U_{\tau 4} | .$ New results obtained in this work
are based on analysis of neutrino mixing matrices obtained from the global fits
at the 95% CL.
