  We decompose a matrix Y into a sum of bilinear terms in a stepwise manner, by
considering Y as a mapping from a finite dimensional Banach space into another
finite dimensional Banach space. We provide transition formulas, and represent
them in a duality diagram, thus generalizing the well known duality diagram in
the french school of data analysis. As an application, we introduce a family of
Euclidean multidimensional scaling models.
