  Oja's algorithm is a well known online algorithm studied mainly in the
context of stochastic principal component analysis. We make a simple
observation, yet to the best of our knowledge a novel one, that when applied to
a any (not necessarily stochastic) sequence of symmetric matrices which share
common eigenvectors, the regret of Oja's algorithm could be directly bounded in
terms of the regret of the well known multiplicative weights update method for
the problem of prediction with expert advice. Several applications to
optimization with quadratic forms over the unit sphere in $\reals^n$ are
discussed.
