diff --git a/report.tex b/report.tex
index 0c9590c..7505db0 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 $i$. $\dim\ker(A - \lambda_i I) \leq m_i$, so we just have to find the condition
+    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 for $\dim\ker(A - \lambda_i I) \geq m_i$. $\dim\ker(A - \lambda_i I) = n - \rank(A - \lambda_i I)$, so we check $\rank(A - \lambda_i I) \leq n - m_i$.
   \end{frame}
 
 \end{document}
\ No newline at end of file