  Suppose that $X_1,\...,X_n,\...$ are i.i.d. rotationally invariant $N$-by-$N$
matrices. Let $\Pi_n=X_n\... X_1$. It is known that $n^{-1}\log |\Pi_n|$
converges to a nonrandom limit. We prove that under certain additional
assumptions on matrices $X_i$ the speed of convergence to this limit does not
decrease when the size of matrices, $N$, grows.
