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Questions about the properties of vector spaces and linear transformations, including linear systems in general.
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Intersection of unit-norm vectors with a large sum in high dimensions with a spherical cap
Let $d$ and $n$ be integers. For $i \in \lbrace 1,\dots,n \rbrace$ let $x_i \in \mathbb{R}^d$ be a vector such that $\lVert x \rVert=1 $. For a fixed $1/2 < \alpha \leq 1$, assume we have $\lVert \sum …