From 733172940bb2e0da98340689d6af8759af3491bd Mon Sep 17 00:00:00 2001
From: Derived Cat <hooyuser@outlook.com>
Date: Sun, 22 Dec 2024 00:41:15 -0500
Subject: [PATCH] Add chapter Vector Space

---
 vector_space.tex | 12 ++++++++++++
 1 file changed, 12 insertions(+)
 create mode 100644 vector_space.tex

diff --git a/vector_space.tex b/vector_space.tex
new file mode 100644
index 0000000..00ee8cc
--- /dev/null
+++ b/vector_space.tex
@@ -0,0 +1,12 @@
+\chapter{Vector Space}
+
+\section{Tensor Product of Vector Spaces}
+\begin{proposition}{}{}
+    Let $V, W$ be vector spaces over a field $K$. If either $V$ or $W$ is finite-dimensional, then we have natural isomorphisms
+    \[
+        \begin{aligned}
+            \mathsf{Hom}_K(V, W) & \cong V^*\otimes W, \\
+            \mathsf{Hom}_K(V, W) & \cong V\otimes W^*.
+        \end{aligned}
+    \]
+\end{proposition}
\ No newline at end of file