Geodesic
Eigenvalue estimates for Hankel matrices
Sbornik. Mathematics, Tome 192 (2001) no. 4, pp. 537-550

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Positive-definite Hankel matrices have an important property: the ratio of the largest and the smallest eigenvalues (the spectral condition number) has as a lower bound an increasing exponential of the order of the matrix that is independent of the particular matrix entries. The proof of this fact is related to the so-called Vandermonde factorizations of positive-definite Hankel matrices. In this paper the structure of these factorizations is studied for real sign-indefinite strongly regular Hankel matrices. Some generalizations of the estimates of the spectral condition number are suggested. 
@article{SM_2001_192_4_a2,
     author = {N. L. Zamarashkin and E. E. Tyrtyshnikov},
     title = {Eigenvalue estimates for {Hankel} matrices},
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     number = {4},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2001_192_4_a2/}
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N. L. Zamarashkin; E. E. Tyrtyshnikov. Eigenvalue estimates for Hankel matrices. Sbornik. Mathematics, Tome 192 (2001) no. 4, pp. 537-550. http://geodesic.mathdoc.fr/item/SM_2001_192_4_a2/