This article gives results specifically related to the last principal component. This linear combination of variables plays an important role when one tries to fit a hyperplane to a cloud of points. In data analysis, variables are often subject to a linear transformation. The results that we...

We examine in this paper various consequences of the Poincari separation theorem. First, Poincari's theorem is used to prove results establishing a constrainted principal component analysis, both at the sample and at the population level. Introduction of constraints in principal component...