Vandermonde factorization and canonical representations of block hankel matrices Original Research Article

We study to which extent well-known facts concerning Vandermonde factorization or canonical representation of scalar Hankel matrices transfer to block Hankel matrices with p × q blocks. It is shown that nonsingular block Hankel matrices can be factored, like in the scalar case, into nonconfluent Vandermonde matrices and that the theorem on full-rank factorization of arbitrary Hankel matrices transfers (in a weak version) to the 2 × 2 block case but not to larger block sizes. In general, the minimal rank of a Vandermonde factorization (both with finite nodes and affine) is described in terms of the Hankel matrix. The main tools are realization, partial realization, and Moebius transformations.