Hankel tensors: Associated Hankel matrices and Vandermonde decomposition

Vandermonde Factorization of a Hankel Matrix ?

We show that an arbitrary Hankel matrix of a nite rank admits a Vandermonde decomposition: H = V T DV , where V is a con-uent Vandermonde matrix and D is a block diagonal matrix. This result was rst derived by Vandevoorde; our contribution here is a presentation that uses only linear algebra, speciically, the Jordan canonical form. We discuss the choices for computing this decomposition in only...

Stable factorization for Hankel and Hankel-like matrices

Determinants of Hankel Matrices

The purpose of this paper is to compute asymptotically Hankel determinants for weights that are supported in a semi-infinite interval. The main idea is to reduce the problem to determinants of other operators whose determinant asymptotics are well known.

Irreducible Toeplitz and Hankel matrices

An infinite matrix is called irreducible if its directed graph is strongly connected. It is proved that an infinite Toeplitz matrix is irreducible if and only if almost every finite leading submatrix is irreducible. An infinite Hankel matrix may be irreducible even if all its finite leading submatrices are reducible. Irreducibility results are also obtained in the finite cases.

Further results on Cauchy tensors and Hankel tensors

In this article, we present various new results on Cauchy tensors and Hankel tensors. We first introduce the concept of generalized Cauchy tensors which extends Cauchy tensors in the current literature, and provide several conditions characterizing positive semi-definiteness of generalized Cauchy tensors with nonzero entries. Furthermore, we prove that all even order generalized Cauchy tensorsw...