Newton's method for solving the matrix equation F(X)≡AX−XXTAX=0 runs
up against the fact that its zeros are not isolated. This is due to a symmetry
of F by the action of the orthogonal group. We show how
differential-geometric techniques can be exploited to remove this symmetry and
obtain a ``geometric'' Newton algorithm that finds the zeros of F. The
geometric Newton method does not suffer from the degeneracy issue that stands
in the way of the original Newton method