Added subsections when they appear, added all of the appendices, and finished the packet

chapter-6/unitary-and-orthogonal-operators-and-their-matrices.tex

@@ -72,6 +72,9 @@
 	\end{enumerate}
 \end{theorem}
 
+\subsection*{Rigid Motions}
+\addcontentsline{toc}{subsection}{Rigid Motions}
+
 \begin{definition}
 	\hfill\\
 	Let $V$ be a real inner product space. A function $f: V \to V$ is called a \textbf{rigid motion} if
@@ -91,6 +94,9 @@
 	Let $f: V \to V$ be a rigid motion on a finite-dimensional real inner product space $V$. Then there exists a unique orthogonal operator $T$ on $V$ and a unique translation $g$ on $V$ such that $f = g \circ T$.
 \end{theorem}
 
+\subsection*{Orthogonal Operators on $\R^2$}
+\addcontentsline{toc}{subsection}{Orthogonal Operators on $\R^2$}
+
 \begin{theorem}
 	\hfill\\
 	Let $T$ be an orthogonal operator on $\R^2$, and let $A = [T]_\beta$ where $\beta$ is the standard ordered basis for $\R^2$. Then exactly one of the following conditions is satisfied:
@@ -106,6 +112,9 @@
 	Any rigid motion on $\R^2$ is either a rotation followed by a translation or a reflection about a line through the origin followed by a translation.
 \end{corollary}
 
+\subsection*{Conic Sections}
+\addcontentsline{toc}{subsection}{Conic Sections}
+
 \begin{definition}
 	Consider the quadratic equation