Eigenvalue estimates for Hankel matrices

Positive-definite Hankel matrices have an important property: the ratio of the largest and the smallest eigenvalues (the spectral condition number) ha s as a lower bound an increasing exponential of the order of the matrix tha t is independent of the particular matrix entries. The proof of this fact i s related to the so-called Vandermonde factorizations of positive-definite Hankel matrices. In this paper the structure of these factorizations is stu died for real sign-indefinite strongly regular Hankel matrices. Some genera lizations of the estimates of the spectral condition number are suggested.