The anisotropic norm of the linear discrete stationary system is the measure of the system output sensitivity to a random input with the mean anisotropy bounded by some nonnegative value a. The mean anisotropy characterizes the degree of predictability of the stochastic signal. The anisotropic norm of a system is the induced norm with the extreme cases of H2 norm and H∞ norm, respectively, under a → 0 and a → ∞. The lower bound of the anisotropic norm of the linear discrete stationary system was established in the present paper using the methods of linear algebra.