\documentclass{article}
\title{Title of Document}
\author{Name of Author}
\begin{document}
\maketitle
\subsection{Definition}
\subsection{Finding solutions}
\subsection{Matrix Operations (algebraic and otherwise)}
\subsection{Matrix equations}
\subsection{The superposition principle}
\subsection{Elementary matrices}
\subsection{Column operations}
\subsection{$\mathbb R^n$}
\subsection{Definition of a vector space}
\subsection{Linear combinations and linear independence}
\subsection{Subspaces}
\subsection{Bases and dimension}
\subsection{Vector spaces over $\mathbb C$}
\subsection{Coordinate vectors}
\subsection{Definition}
\subsection{Matrix representations of transformations}
\subsection{Change of basis}
\subsection{The dot product in $\mathbb R^n$}
\subsection{Symmetric bilinear pairings on $\mathbb R^n$, and their representation}
\subsection{Orthogonal vectors and subspaces in $\mathbb R^n$}
\subsection{Projections onto subspaces and Gram-Schmidt orthogonalization}
\subsection{Least-squares approximations}
\subsection{Least-squares solutions and the Fundamental Subspaces theorem}
\subsection{Applications of least-squares solutions}
\subsection{The complex scalar product in $\mathbb C^n$}
\subsection{Conjugate-symmetric sesquilinear pairings on $\mathbb C^n$, and their representation}
\subsection{Unitary matrices}
\subsection{Definition}
\subsection{The determinant}
\subsection{The characteristic polynomial}
\subsection{Eigenspaces}
\subsection{Direct sum decomposition}
\subsection{Similarity and diagonalization}
\subsection{Complex eigenvalues and eigenvectors}
\subsection{Geometric vs algebraic multiplicity}
\subsection{Shur's Theorem}
\end{document}