deletions | additions       diff --git a/subsection_Non_convex_optimization_formulation__.tex b/subsection_Non_convex_optimization_formulation__.tex  index 5fd72b5..7aabfdf 100644  --- a/subsection_Non_convex_optimization_formulation__.tex  +++ b/subsection_Non_convex_optimization_formulation__.tex 
...
\paragraph{Symmetry and reduction}   \begin{enumerate}  \item When $\mathbf{A}_0$ is not orthogonal, it can be reduced to the orthogonal case by preconditioning $\hat{\mathbf{Y}} = \big(\frac{1}{p \theta} \mathbf{Y} \mathbf{Y}^T \big)^{-1/2} \mathbf{Y}$. \mathbf{Y}$ for some $i \in [n]$ and $\alpha \neq 0$.  \item All orthogonal $\mathbf{A}_0$ are equivalent since $f(\mathbf{q}; \mathbf{A}_0 \mathbf{X}_0) = f(\mathbf{A_0}^T \mathbf{q}; \mathbf{X}_0)$, corresponding to a rotation on $\mathbf{q}$.