Formal vector orthogonal polynomials

The aim of this paper is to define and to study orthogonal polynomials with respect to a linear functional whose moments are vectors. We show how a Clifford algebra allows us to construct such polynomials in a natural way. This new definition is motivated by the fact that there exist natural links between this theory of orthogonal polynomials and the theory of the vector valued Padé approximants in the sense of Graves-Morris and Roberts. This revised version was published online in June 2006 with corrections to the Cover Date.