VANDERMONDE FACTORIZATION AND CANONICAL REPRESENTATIONS OF BLOCK HANKEL-MATRICES

We study to which extent well-known facts concerning Vandermonde facto rization or canonical representation of scalar Hankel matrices transfe r to block Hankel matrices with p x q blocks. It is shown that nonsing ular block Hankel matrices can be factored, like in the scalar case, i nto nonconfluent Vandermonde matrices and that the theorem on full-ran k factorization of arbitrary Hankel matrices transfers (in a weak vers ion) to the 2 x 2 block case but not to larger block sizes. In general , the minimal rank of a Vandermonde factorization (both with finite no des and affine) is described in terms of the Hankel matrix. The main t ools are realization, partial realization, and Moebius transformations .