  We derive sharp non - asymptotical Lebesgue - Riesz as well as Grand Lebesgue
Space norm estimations for different norms of matrix martingales through these
norms for the correspondent martingale differences and through the entropic
dimension of the extremal points of the unit ball for a basic space. These
estimates allow us to deduce in particular the exponential decreasing tail of
distribution for these norms of matrix martingales. We bring also some examples
in order to show the exactness of the obtained estimations.
