关于S-矩阵猜想
On the S-matrix conjecture
摘要：
出于光谱学中的一个问题，Sloane和Harwit在1976年证明了所有元素都来自区间[0，1]的矩阵的逆的最小Frobenius范数是什么。在1987年，程证明了他们的猜想的情况下，奇数维，而偶数维，他得到了一个稍微弱下界的规范。他的证明基于最优设计近似理论中的基弗-沃尔福威茨等价定理。本文给出了这个结果的一个简短的证明。
英文摘要：
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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