The Lagrangian on the last page associated with computing the maximal eigenpair should probably have the term lamba (x^T x - 1), not lamba x^T x. The latter get

The Lagrangian on the last page associated with computing the maximal eigenpair should probably have the term lamba (x^T x - 1), not lamba x^T x. The latter gets the gradient with respect to x right, but not the gradient with respect to lambda, and it would provide the wrong dual problem.