  In this paper we analyze the behavior of the Oja's algorithm for
online/streaming principal component subspace estimation. It is proved that
with high probability it performs an efficient, gap-free, global convergence
rate to approximate an principal component subspace for any sub-Gaussian
distribution. Moreover, it is the first time to show that the convergence rate,
namely the upper bound of the approximation, exactly matches the lower bound of
an approximation obtained by the offline/classical PCA up to a constant factor.
