My question concerns the name for determinants of Hankel-matrices $H = (s_{i+j})_{i,j = 0}^n$.

In the classical textbook of Shohat and Tamarkin (1943) "The Problem of Moments", these determinants are defined without a name (on page viii).

In several math articles, I found the name Hankel determinant. In the field of physics (especially methods of moments), where I work, however, the common name seems to be "Hankel-Hadamard determinant"

Does anyone can give me a hint on how Hadamard is connected to this? Any help would be highly appreciated!


Some background is given in the appendix of this 1988 paper by Handy and Bessis, who apparently introduced this terminology: Hankel-Hadamard matrix, Hankel-Hadamard determinant, Hankel-Hadamard positivity, Hankel-Hadamard inequality. It refers to a class of matrices of the Hankel form (constant diagonals) with a determinant that satisfies a generalized Hadamard inequality. The inequality is not quite the original Hadamard inequality (it's a lower bound rather than an upper bound on the determinant), but the name stuck.

  • $\begingroup$ @Carlo Thank you very much indeed! I stumbled across the Handy and Bessis (1988) paper quite frequently when looking for an answer myself. As my institute does not subscribe to the APS "Physical Review A" Journal, however, I could not see the contents. Now I will try to get hold of a copy via interlibrary loan. Thanks again!! $\endgroup$ – Maria Z Jun 20 '13 at 6:51

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