
\subsection{\bf Types of Matrices}

\begin{slide}

\begin{itemize}
\item Useful Symbols

$A^T = \mbox{Transpose} \hspace{2em} \left( A^T \right)_{ij} =
A_{ji}$

$A^* = \mbox{Complex\ Conjugate} \hspace{1em} \left( A^*
\right)_{ij} = A^*_{ij}$

$A^+ = \mbox{Hermitean Conjugate} \hspace{1em} \left( A^+
\right)_{ij} = A^*_{ji}$

\item $A = A^+$ \hspace{2em} Hermitean Matrix

\item In physics, all nice matrices are hermitean---we can
understand why when we study eigenvalues and eigenvectors.

\item Hermitean operators have a complete set of eigenvectors with
real eigenvalues.
\end{itemize}

\end{slide}

