  We consider a situation in which we see samples in $\mathbb{R}^d$ drawn
i.i.d. from some distribution with mean zero and unknown covariance A. We wish
to compute the top eigenvector of A in an incremental fashion - with an
algorithm that maintains an estimate of the top eigenvector in O(d) space, and
incrementally adjusts the estimate with each new data point that arrives. Two
classical such schemes are due to Krasulina (1969) and Oja (1983). We give
finite-sample convergence rates for both.
