diff --git a/report.tex b/report.tex
index 2d4e43e..f51aa0d 100644
--- a/report.tex
+++ b/report.tex
@@ -340,7 +340,11 @@
         -\gamma \myvec{\xi} & -\myvec{\xi} & 0
       \end{pmatrix},
     \end{equation}
-    which is no longer symmetric, but luckily it's still diagonalizable with real eigenvalues, and thus the system is still strongly hyperbolic, and well-posed in the $L^2$ sense.
+    which is no longer symmetric, but luckily it's still diagonalizable with exactly the same eigenvalues, and the eigenvectors are also almost the same, except that
+    \begin{equation}
+      \myvec{e}_1 = \mqty(1,-\gamma,0,0,0)^T,
+    \end{equation}
+    and thus the system is still strongly hyperbolic, and well-posed in the $L^2$ sense.
   \end{frame}
 
   \begin{frame}{Existing first order formulations}