From 5a92976b1c59fcaafece96a29596b0b8565a05ba Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Thu, 9 Apr 2026 21:25:43 -0400
Subject: [PATCH] update: auto commit

---
 report.tex | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/report.tex b/report.tex
index f64cc05..2f4126f 100644
--- a/report.tex
+++ b/report.tex
@@ -341,6 +341,14 @@
       \end{pmatrix} \qc
       S=-\gamma \mqty(0 \\ 0 \\ \myvec{\psi}),
     \end{equation}
+    thus the principal symbol matrix is
+    \begin{equation}
+      \tensor{P}{^I_J}(\xi) = \begin{pmatrix}
+        0 & 0 & 0 \\
+        0 & 0 & -\myvec{\xi}^T \\
+        -\gamma \myvec{\xi} & -\myvec{\xi} & 0
+      \end{pmatrix},
+    \end{equation}
   \end{frame}
 
   \begin{frame}{Existing first order formulations}