Finished all chapters and definitions. I need to add subsections and see if there's any theorems or definitions in the appendicies that are worth adding to this as well.

chapter-2/the-change-of-coordinate-matrix.tex

@@ -3,7 +3,7 @@
 \begin{theorem}\label{Theorem 2.22}
 	\hfill\\
 	Let $\beta$ and $\beta'$ be two ordered bases for a finite-dimensional vector pace $V$, and let $Q = [I_V]_{\beta'}^\beta$. Then
-	
+
 	\begin{enumerate}
 		\item $Q$ is invertible.
 		\item For any $v \in V$, $[v]_\beta = Q[v]_{\beta'}$.
@@ -23,11 +23,11 @@
 \begin{theorem}
 	\hfill\\
 	Let $T$ be a linear operator on a finite-dimensional vector space $V$, and let $\beta$ and $\beta'$ be ordered bases for $V$. Suppose that $Q$ is the change of coordinate matrix that changes $\beta'$-coordinates into $\beta$-coordinates. Then
-	
+
 	\[[T]_{\beta'}=Q^{-1}[T]_\beta Q\]
 \end{theorem}
 
-\begin{corollary}
+\begin{corollary}\label{Corollary 2.8}
 	\hfill\\
 	Let $A \in M_{n \times n}(\F)$, and let $\gamma$ be an ordered basis for $\F^n$. Then $[L_A]_\gamma = Q^{-1}AQ$, where $Q$ is the $n \times n$ matrix whose $j$th column is the $j$th vector of $\gamma$.
 \end{corollary}
@@ -35,6 +35,6 @@
 \begin{definition}
 	\hfill\\
 	Let $A$ and $B$ be matrices in $M_{n \times n}(\F)$. We say that $B$ is \textbf{similar} to $A$ if there exists an invertible matrix $Q$ such that $B = Q^{-1}AQ$.\\
-	
+
 	Notice that the relation of similarity is an equivalence relation. So we need only say that $A$ and $B$ are similar.
-\end{definition}
+\end{definition}