Minor adjustments.

src/fa/tvs/complexify.tex

@@ -84,6 +84,18 @@
     
 \end{proof}
 
+\begin{definition}[Hermitian]
+\label{definition:hermitian-functional}
+    Let $E$ be a vector space over $\real$, $*: \complex(E) \to \complex(E)$ be the canonical complex conjugation map, and $\phi \in \hom(\complex(E); \complex)$, then the following are equivalent: 
+    \begin{enumerate}
+        \item $\phi|_E \in \hom(E; \real)$.
+        \item For each $x \in E$, $\dpn{x, \phi}{\complex(E)} = \ol{\dpn{x^*, \phi}{\complex(E)}}$. 
+    \end{enumerate}
+
+    If the above holds, then $\phi$ is \textbf{Hermitian}.     
+\end{definition}
+
+