From 4b862c61f8ea14f508e168062499d11018e5a7a7 Mon Sep 17 00:00:00 2001
From: Glen Whitney <glen@nobody@nowhere.net>
Date: Wed, 19 Feb 2025 16:15:46 +0000
Subject: [PATCH] Update Gram matrix parameterization

---
 Gram-matrix-parameterization.md | 7 +------
 1 file changed, 1 insertion(+), 6 deletions(-)

diff --git a/Gram-matrix-parameterization.md b/Gram-matrix-parameterization.md
index f9987e2..e4c4752 100644
--- a/Gram-matrix-parameterization.md
+++ b/Gram-matrix-parameterization.md
@@ -39,12 +39,7 @@ on $\operatorname{Hom}(\mathbb{R}^n, V)$. Finding a global minimum of the *loss
 #### The first derivative of the loss function
 
 Write the loss function as
-\[
-\begin{align*}
-f & = \|\Delta\|^2 \\
-& = \operatorname{tr}(\Delta^\top \Delta),
-\end{align*}
-\]
+\[ \begin{align*} f & = \|\Delta\|^2 \\ & = \operatorname{tr}(\Delta^\top \Delta), \end{align*} \]
 where $\Delta = G - \mathcal{P}(A^\top Q A)$. Differentiate both sides and simplify the result using the transpose-invariance of the trace:
 \[
 \begin{align*}