\( \lambda:=\operatorname{solve}(|A-\lambda \cdot E|=0 ; \lambda)=\left[\begin{array}{l}1 \\ 2\end{array}\right] \)
\( \lambda_{1}=1 \)
DimEigenraum \( ==\left(n-\operatorname{rank}\left(A-\lambda_{1} \cdot E\right)\right)=1 \)
\( E V \lambda 1:=\left(A-\lambda_{1} \cdot E\right)=\left[\begin{array}{lll}-2 & 1 & 1 \\ -3 & 2 & 1 \\ -3 & 1 & 2\end{array}\right] \)
\( E V11:=\operatorname{RRef}(E V \lambda 1)=\left[\begin{array}{ccc}1 & 0 & -1 \\ 0 & 1 & -1 \\ 0 & 0 & 0\end{array}\right] \)
\(EV11 \cdot X=\left[\begin{array}{c}x 1-x 3 \\ x 2-x 3 \\ 0\end{array}\right] \)
\(EV10 : = \left[\begin{array}{c}1 \\ 1 \\ 1\end{array}\right] \)
\( \lambda_{2}=2 \)
DimEigenraum \( :=\left(n-\operatorname{rank}\left(A-\lambda_{2} \cdot E\right)\right)=2 \)
\( E V \lambda 2:=\left(A-\lambda_{2} \cdot E\right)=\left[\begin{array}{lll}-3 & 1 & 1 \\ -3 & 1 & 1 \\ -3 & 1 & 1\end{array}\right] \)
\( E V 21:=R \operatorname{Ref}(E V \lambda 2)=\left[\begin{array}{ccc}1 & -\frac{1}{3} & -\frac{1}{3} \\ 0 & 0 & 0 \\ 0 & 0 & 0\end{array}\right] \)
\( E V 21 \cdot X=\left[\begin{array}{c}-\frac{x 2-3 \cdot x 1+x 3}{3} \\ 0 \\ 0\end{array}\right] \)
\( E V 20:=E V 22_{3}=\left[\begin{array}{cc}\frac{1}{3} & \frac{1}{3} \\ 1 & 0 \\ 0 & 1\end{array}\right] \)
\(T:= \left[\begin{array}{lll}1 & \frac{1}{3} & \frac{1}{3} \\ 1 & 1 & 0 \\ 1 & 0 & 1\end{array}\right] \)
\( T^{-1} \cdot A \cdot T=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right] \)
Analog für b - gleiche EW - EW 1 wie a) - EW 2 DimEigenraum=1 - nicht dialogisierbar
