From 3c5c74dc221e26ffae1c14d093fe9b64f423ae58 Mon Sep 17 00:00:00 2001
From: Yingjie Wang <phywyj@gmail.com>
Date: Fri, 10 Apr 2026 03:10:30 -0400
Subject: [PATCH] update: auto commit

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

diff --git a/report.tex b/report.tex
index 8258a1e..0c9590c 100644
--- a/report.tex
+++ b/report.tex
@@ -919,7 +919,7 @@ $}
   \end{frame}
 
   \begin{frame}{Appendix}{Why can't we fully automate the workflow using Mathematica?}
-    The correct way is to check the geometric multiplicity for each eigenvalues. Say we get eigenvalues $\lambda_1, ..., \lambda_k$ with the algebraic multiplicity $m_1, ..., m_k$. Under the assumption that all these eigenvalues are different from each other, we check $\dim\ker(A - \lambda_i I)$ for each $i$.
+    The correct way is to check the geometric multiplicity for each eigenvalues. Say we get eigenvalues $\lambda_1, ..., \lambda_k$ with the algebraic multiplicity $m_1, ..., m_k$. Under the assumption that all these eigenvalues are different from each other, we check $\dim\ker(A - \lambda_i I)$ for each $i$. $\dim\ker(A - \lambda_i I) \leq m_i$, so we just have to find the condition
   \end{frame}
 
 \end{document}
\ No newline at end of file