diff --git a/src/fa/norm/hilbert.tex b/src/fa/norm/hilbert.tex
index d652dc3..21f82b5 100644
--- a/src/fa/norm/hilbert.tex
+++ b/src/fa/norm/hilbert.tex
@@ -373,7 +373,7 @@ A significant property of Hilbert spaces is that every closed subspace is comple
 \label{definition:hilbert-quadratic-function}
     Let $H$ be a complex Hilbert space and $q: H \to \complex$, then $q$ is \textbf{quadratic} if:
     \begin{enumerate}
-        \item For each $\lambda \in \complex$ and $\xi \in H$, $q(\lambda x) = |\lambda|^2 q(\xi)$. 
+        \item For each $\lambda \in \complex$ and $\xi \in H$, $q(\lambda \xi) = |\lambda|^2 q(\xi)$. 
         \item (\textbf{Parallelogram Law}) For each $\xi, \eta \in H$, 
         \[
         q(\xi + \eta) + q(\xi - \eta) = 2q(\xi) + 2q(\eta)
diff --git a/src/op/system/schur.tex b/src/op/system/schur.tex
index 2f746ad..a371b40 100644
--- a/src/op/system/schur.tex
+++ b/src/op/system/schur.tex
@@ -70,7 +70,7 @@
 
     (T2) $\Rightarrow$ (T1): For each $n \in \natp$, 
     \begin{align*}
-    0 &\le \braks{\sum_{j = 1}^n E_{1j} \otimes z^j}^*\braks{\sum_{j = 1}^n E_{1j} \otimes z^j} = \sum_{j, k = 1}^n E_{jk} \otimes z^{j-k} \\
+    0 &\le \braks{\sum_{j = 1}^n E_{j1} \otimes z^j}\braks{\sum_{j = 1}^n E_{j1} \otimes z^j}^* = \sum_{j, k = 1}^n E_{jk} \otimes z^{j-k} \\
     0 &\le \phi\braks{\sum_{j, k = 1}^n E_{jk} \otimes z^{j-k}} = \sum_{j, k = 1}^n E_{jk} \otimes A_{j - k}
     \end{align*}
 \end{proof}
\ No newline at end of file