Factorization of finite rank Hankel and Toeplitz matrices

The main purpose of this paper is to prove factorization results for finite Hankel and Toeplitz matrices that generalize known results for the positive semidefinite case. Generalized Vandermonde matrices appear in the factorizations. Factorization theorems are proved for infinite Hankel and Toeplitz matrices of finite rank, and the results for finite matrices are deduced via a technique of rank-preserving extension.