Within the last years various principal component analysis (PCA) algorithms have been proposed. In this paper we use a general framework to describe those PCA algorithms which are based on Hebbian learning. For an important subset of these algorithms, the local algorithms, we fully describe their equilibria, where all lateral connections are set to zero and their local stability. We show how the parameters in the PCA algorithms have to be chosen in order to get an algorithm which converges to a stable equilibrium which provides principal component extraction.