On the S-matrix conjecture
Functional Analysis
2013-12-10 v2
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.
Keywords
Cite
@article{arxiv.1306.6786,
title = {On the S-matrix conjecture},
author = {Roman Drnovšek},
journal= {arXiv preprint arXiv:1306.6786},
year = {2013}
}
Comments
minor changes; to appear in Linear Algebra and its Applications