% <PLAINTEXT>
% $BNL;RJ*M}3X(B $B!'(B $B1i=,LdBj(B 3-1 $B2rEz(B
% $B:n(B  $B@.(B  $B<T(B $B!'(B g040496 $B>BED(B $BOB9,(B
% $B:n@.G/7nF|(B $B!'(B 00/12/06
% $BEE;R%a!<%k(B $B!'(B g040496@mail.ecc.u-tokyo.ac.jp
%
\mondai
{g040496 $B>BED(B $BOB9,(B}
{01/01/30}
{g040496@mail.ecc.u-tokyo.ac.jp}
{3-1}
{$B<!$N%(%k%_!<%H9TNs$N8GM-CM!"8GM-%Y%/%H%k$r5a$a$h!#(B
$$ (a) \ \ 
\left( \begin{array}{cc} 
	 0 & 1 \\
	 1 & 0 
\end{array} \right) \ \ 
(b) \ \ 
\left( \begin{array}{cc}
 	 1 & i \\
 	-i & 1 
\end{array} \right) $$
}
{ (a) 
\begin{equation}
\left| \begin{array}{cc}
	\lambda & -1 \\
	-1 & \lambda
\end{array} \right|
= \lambda^2 -1 = (\lambda +1)(\lambda -1) = 0
\end{equation}
$B$h$C$F8GM-CM$O(B\ \ $\lambda = \pm 1$\ \ $B$G$"$j!"3F!9$KBP$9$k8GM-%Y%/%H%k$O(B
\begin{equation}
{\bf u}_1 = \alpha \left( \begin{array}{c} 1 \\ 1 \end{array} \right) \ \ ,\ 
{\bf u}_2 = \beta \left( \begin{array}{c} 1 \\ -1 \end{array} \right)
\end{equation}
$B$H$J$k!#C10L%Y%/%H%k$KD>$;$P0J2<$NDL$j!#(B
\begin{equation}
	{\bf u}_1 = \frac{1}{\sqrt{2}} \left( \begin{array}{c} 1 \\ 1 \end{array} \right) \ \ ,\ 
{\bf u}_2 = \frac{1}{\sqrt{2}} \left( \begin{array}{c} 1 \\ -1 \end{array} \right)
\end{equation}
\\
(b) \\
\begin{equation}
\left| \begin{array}{cc}
	\lambda -1 & -i \\
	i & \lambda -1
\end{array} \right|
= \left( \lambda -1 \right)^2 - (-i)i= \lambda (\lambda -2) = 0
\end{equation}
$B8N$K8GM-CM$O(B\ \ $\lambda = 0 , 2$\ \ $B$G$"$j!"3F!9$KBP$9$k8GM-%Y%/%H%k$O(B
\begin{equation}
{\bf u}_1 = \alpha \left( \begin{array}{c} 1 \\ i \end{array} \right) \ \ ,\ 
{\bf u}_2 = \beta \left( \begin{array}{c} i \\ 1 \end{array} \right)
\end{equation}
$B$H$J$k!#C10L%Y%/%H%k$KD>$;$P0J2<$NDL$j!#(B
\begin{equation}
	{\bf u}_1 = \frac{1}{\sqrt{2}} \left( \begin{array}{c} 1 \\ i \end{array} \right) \ \ ,\ 
{\bf u}_2 = \frac{1}{\sqrt{2}} \left( \begin{array}{c} i \\ 1 \end{array} \right)
\end{equation}
}
