This paper gives a generalization of results presented by ten Berge, Krijnen, Wansbeek & Shapiro. They examined procedures and results as proposed by Anderson & Rubin, McDonald, Green and Krijnen, Wansbeek & ten Berge. We shall consider the same matter, under weaker rank assumptions. We allow some moments, namely the variance of the observable scores vector and that of the unique factors,to be singular. We require T′ T > 0, where T T′ is a Schur decomposition of. As usual the variance of the common factors, , and the loadings matrix Awill have full column rank.