
\subsection{\bf Definition of a Matrix}

\begin{slide}

\begin{itemize}
\item Consider matrix with elements $A_{ij}$

\item It is an operator {\fifteenbxti A} in a vector space of dimension $n$
where {\fifteenbxti A} is $n\times n$.

\item There are $n^2$ numbers $A_{ij}$ defining {\fifteenbxti A}.

\item The vector space is spanned by a ``complete basis''
$\underline{e}_{\underline{k}}$, $k=1 \ldots n$.

\item One choice of $\underline{e}_k$ is
\begin{eqnarray*}
\underline{e}_1 & = & ( 1, 0, 0, \ldots 0 ) \\
\underline{e}_2 & = & ( 0, 1, \ldots 0 ) \\
\underline{e}_n & = & ( 0, 0, \ldots 1 )
\end{eqnarray*} 
\end{itemize}

\end{slide}

