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arXiv · 1306.6786

On the S-matrix conjecture

Roman Drnovšek
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Abstract

Motivated with a problem in spectroscopy, Sloane and Harwit conjectured in 1976 what is the minimal Frobenius norm of the inverse of a matrix having all entries from the interval [0, 1]. In 1987, Cheng proved their conjecture in the case of odd dimensions, while for even dimensions he obtained a slightly weaker lower bound for the norm. His proof is based on the Kiefer-Wolfowitz equivalence theorem from the approximate theory of optimal design. In this note we give a short and simple proof of his result.

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Roman Drnovšek. 2013-06-28. On the S-matrix conjecture. https://arxiv.org/abs/1306.6786

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