The eigenvectors of \(A = \left( {\begin{array}{*{20}{c}} 0&{ - 1}\\ 1&0 \end{array}} \right)\) are:
1
\(\left( {\begin{array}{*{20}{c}}
1\\
{ - i}
\end{array}} \right),\left( {\begin{array}{*{20}{c}}
1\\
i
\end{array}} \right)\)
2
\(\left( {\begin{array}{*{20}{c}}
1\\
0
\end{array}} \right)\left( {\begin{array}{*{20}{c}}
{ - 1}\\
0
\end{array}} \right)\)
3
\(\left( {\begin{array}{*{20}{c}}
0\\
1
\end{array}} \right),\left( {\begin{array}{*{20}{c}}
{ - 1}\\
0
\end{array}} \right)\)
4
\(\left( {\begin{array}{*{20}{c}}
i\\
{ - i}
\end{array}} \right),\left( {\begin{array}{*{20}{c}}
1\\
{ - 1}
\end{array}} \right)\)