摘要
A finite collection of unit vectors S ⊂ ℝn is called a spherical two-distance set if there are two numbers a and b such that the inner products of distinct vectors from S are either a or b. We prove that if a ≠ -b, then a two-distance set that forms a tight frame for ℝn is a spherical embedding of a strongly regular graph. We also describe all two-distance tight frames obtained from a given graph. Together with an earlier work by S. Waldron (2009) [22] on the equiangular case, this completely characterizes two-distance tight frames. As an intermediate result, we obtain a classification of all two-distance 2-designs.
原文 | ???core.languages.en_GB??? |
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文章編號 | 13109 |
頁(從 - 到) | 163-175 |
頁數 | 13 |
期刊 | Linear Algebra and Its Applications |
卷 | 475 |
DOIs | |
出版狀態 | 已出版 - 6月 2015 |