Vandermonde factorization and canonical representations of block Hankel matrices
The aim of this paper is to generalize some well-known results from the theory of Hankel matrices from the scalar of the block case. The authors extend \textit{M. Tismenetsky's} results [ibid. 166, 45-63 (1992; Zbl 0762.15005)] into two directions. First, they prove that nonsingular block Hankel matrices admit a Vandermonde factorization with nonconfluent Vandermonde matrices and a diagonal matrix as the middle factor. The corresponding theorem is formulated in Section 3 and proved in Section 6. Second, they discuss Vandermonde factorization of arbitrary block Hankel matrices or canonical representation of arbitrary sequences of blocks, which is the same. In Section 4 they show that full rank Vandermonde factorization of infinite block Hankel matrices is a simple consequence of the minimal realization of the corresponding sequences of blocks considered as the Markov parameters of a linear time invariant system. Similarly, in Section 5 it is shown that the Vandermonde factorization with finite nodes is a consequence of the solution of the partial realization problem for the underlying sequence blocks. Moebius transformations of block Hankel and Vandermonde matrices and of Vandermonde factorizations of block Hankel matrices are studied in Section 7.
scientific article; zbMATH DE number 931891
scientific article