All Questions

Let $N=\{1,2,\ldots,n\}$. Suppose we are given $n$ equations, with each equation taking the form $\sum_{A\subseteq N}\left(c_A \prod_{i\in A}x_i \right) = 0$, where each $c_A$ is a real number ...

Suppose we have n normalized vectors on an arbitrarily large Hilbert space $|A_1\rangle,\dots,|A_n\rangle$, $\langle A_i|A_i\rangle=1$ for every i. And there're $\frac{n(n-1)}{2}$ inner products $\...