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Next, we summarize some of the key properties of this problem, which are later formalized by the paper.   \begin{enumerate}  \item When $A_0$ is orthogonal, $f(\mathbf{q}, \mathbf{Y})$ has no spurious local minima. In fact, each local minimizer $\hat{\mathbf{q}}$ corresponds to a row of $\mathbf{X}_0$ by $\hat{\mathbf{q}}^T \mathbf{Y} = \alpha \mathbf{e}_i^T \mathbf{X}_0$.  \item The feasible region $\mathbf{q} \in \mathbb{S}^{n-1}$ is a sphere with $2n$ symmetric sections, corresponding to those centered around $\pm \mathbf{e}_i$ for $i=1,\cdots,n$.   \item