Add chapter Vector Space

vector_space.tex

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+\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}