abstract-algebra-theorems-and-definitions/part-4/chapters/chapter-19/subspaces.tex

\section{Subspaces}

\begin{definition}[Subspace]
	Let $V$ be a vector space over a field $\F$ and let $U$ be a subset of $V$. We say that $U$ is a \textit{subspace} of $V$ if $U$ is also a vector space over $\F$ under the operations of $V$.
\end{definition}