Is there an upper bound on the number of vectors in $\mathbb{R}^n$ such that the angle between any two vectors are at least $\alpha$?

23 Views Asked by At

Suppose that $\alpha >0$ is a fixed constant, $v_1,v_2,\cdots ,v_N$ are vectors in $\mathbb{R}^n$, and for any $1 \leq i < j \leq N$, the angle between $v_i$ and $v_j$ are at least $\alpha$. I'm curious about whether there exists and upper bound on $N$ in terms of $\alpha$ and $n$. Can anyone help please?