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When can a point be reconstructed from relative angle measurements?

Given a set of points $p_1,\dots,p_n$ in $\mathbb{R}^d$ and a target point $x\in\mathbb{R}^d$, I measure all the angles between all pairs of points and the target point. In other words, I have the ...
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Maximize the product of Hadamard matrix and a vector

Let $X$ be an $n \times n$ Hadamard matrix (i.e. entries are in $\{-1,1\}$ and rows are orthogonal). For my application, we can assume $n=2^k$. Given a vector $\bf{w} \in R^n$, I want to find the $X^*$...