\[\lambda = 0 - 2i\] \[C = \begin{bmatrix} 0 & -2 \\ 2 & 0 \end{bmatrix}\] \[A = \begin{bmatrix} -1 & -3 \\ -1 & -4 \end{bmatrix} \begin{bmatrix} 0 & -2 \\ 2 & 0 \end{bmatrix} \begin{bmatrix} -4 & 3 \\ 1 & -1 \end{bmatrix}\]

Problem:

Write \(A = P C P^{-1}\) for the matrix 
\[A = \begin{bmatrix} 
26 & -20   \\ 
34 & -26
\end{bmatrix},\]
with \(C\) a rotation matrix corresponding to a complex eigenvalue \(\lambda = a + b i\).

\begin{solution}
Solution:
\[\lambda = 0 - 2i\]
\[C = \begin{bmatrix} 
0 & -2   \\ 
2 & 0
\end{bmatrix}\]
\[A = \begin{bmatrix} 
-1 & -3   \\ 
-1 & -4
\end{bmatrix} \begin{bmatrix} 
0 & -2   \\ 
2 & 0
\end{bmatrix} \begin{bmatrix} 
-4 & 3   \\ 
1 & -1
\end{bmatrix}\]
\end{solution}