
\subsection{\bf Eigenvectors and Eigenvalues of}
\subsection{\bf Symmetric Matrices}

\begin{slide}

\begin{itemize}
\item Above we have taken hermitean operator $A^+ = A$.  If $A$
real then $A^+ = A^T$ and $A^T = A$.

\item Then eigen$\underline{\rm vectors}$ can be taken to be real
as equation $(A-\lambda_i I) | v_k >$ has real coefficients (we
showed $\lambda_k$ real).

\item Then $U$ is real
\begin{eqnarray*}
U^+ & = & U^T \\
U^T U & = & I \\
U & \mbox{is} & \mbox{ORTHOGONAL}
\end{eqnarray*}
\end{itemize}

\end{slide}

