What is a vector Hankel determinant

AbstractIn this paper, a Hankel determinant whose entries belong to a real finite dimensional vector space is defined. Such a Hankel determinant appears, purely as a computational process result (lacking of any property), in the algebraic approach to the vector ε-algorithm and in the theory of vector orthogonal polynomials. The aim of this paper is to give an independent study of these determinants, involving their fundamental algebraic properties