Add notes on operators.

reference/all-the-maths-we-know.tex

@@ -289,7 +289,7 @@ \section*{Linear maps}
 
 %% ============================================================
 
-\section*{Quotient spaces}
+\section*{Quotient space}
 \begin{tabularx}{\columnwidth}{@{}l>{\raggedright\arraybackslash}X@{}}
   \toprule
   \defn{$a+U$} & The set $\{a+u\mid u\in U\}$. What you get by “translating” $U$ by~$a$.  \\ 
@@ -397,5 +397,24 @@ \section*{Matrices}
 
 \end{tabularx}
 
+%% ============================================================
+
+\section*{Operators}
+\begin{tabularx}{\columnwidth}{@{}l>{\raggedright\arraybackslash}X@{}}
+  \toprule
+  \defn{Operator} & A linear map from a vector space to itself. \\
+
+  \parbox[t]{\termheaderwd}{\defn{Invariant\\ subspace}} & Of an operator, $T\colon V\to V$. A subspace $U$ of $V$ is invariant under $T$ if $T u\in U$ for all $u\in U$. \\
+
+  \defn{Eigenvalue} &
+                      Of an operator, $T$. A number $\lambda$ such that there exists a vector $v\neq 0$ with $Tv=\lambda v$. 
+
+                      (The vector $v$ is called an \emph{eignvector}.)
+
+
+  \\ 
+
+\end{tabularx}
+
 \end{multicols*}
 \end{document}