相关阵集的单纯形面
Simplicial faces of the set of correlation matrices
摘要：
本文研究了$n \times n$相关阵集的人脸几何。主要结果表明，几乎每一组$r$顶点生成一个单纯面，只要$r \leq \sqrt{\mathrm{c} n}$，其中$\mathrm{c}$是一个绝对常数。这个界限定性上是尖锐的，因为相关阵的集合没有由多于$\sqrt{2n}$顶点生成的单纯面。
英文摘要：
This paper concerns the facial geometry of the set of $n \times n$ correlation matrices. The main result states that almost every set of $r$ vertices generates a simplicial face, provided that $r \leq \sqrt{\mathrm{c} n}$, where $\mathrm{c}$ is an absolute constant. This bound is qualitatively sharp because the set of correlation matrices has no simplicial face generated by more than $\sqrt{2n}$ vertices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
