From e4d0579011fc6d327aba9f8668ae4afd0accd4fc Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Thu, 9 Apr 2026 20:20:34 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/report.tex b/report.tex
index 1e40865..bda474a 100644
--- a/report.tex
+++ b/report.tex
@@ -272,8 +272,9 @@
         0 & 0 & -\tensor{e}{_i} \\
         0 & -\tensor{e}{^i} & 0
       \end{pmatrix} \qc
-      S=0.
+      S=0,
     \end{equation}
+    where $\tensor{e}{^i}$ is the standard column vector basis of $\mathbb{R}^3$, while $\tensor{e}{_i}$ is the standard row vector basis of $(\mathbb{R}^3)^*$.
   \end{frame}
 
   \begin{frame}{Existing first order formulations}