Hankel 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.

Stable factorization for Hankel and Hankel-like matrices

Small eigenvalues of large Hankel matrices

In this paper we investigate the smallest eigenvalue, denoted as λN , of a (N+1)×(N+1) Hankel or moments matrix, associated with the weight, w(x) = exp(−xβ), x > 0, β > 0, in the large N limit. Using a previous result, the asymptotics for the polynomials, Pn(z), z / ∈ [0,∞), orthonormal with respect to w, which are required in the determination of λN are found. Adopting an argument of Szegö the...

Hankel Matrices for Weighted Visibly Pushdown Automata