All Questions

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 ...

Wahba's problem is the following: $$\min_R \sum_{k=1}^K \|v_k - Rw_k\|^2$$ where $v_k$ and $w_k$ are arbitrary $3\times 1$ vectors, and $R$ is a rotation matrix (i.e., orthogonal with $\det(R)=1$). A ...

Let $A,B \in R^{n\times r}$ with $A^\top B $ invertible. It is known that \begin{equation} UV^\top :=\arg\min_{R \in \mathcal{O}^{r\times r}}\|AR-B\|_\mathrm{F}, \end{equation} where $USV^\top$ is ...