Mo logo [home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff] german flag
Mathematics-Online course: Linear Algebra - Normal Forms - Jordan Normal Form

Jordan Form of (4x4)-Matrices

[previous page] [next page] [table of contents][page overview]
The following picture shows the $ 14$ possible Jordan forms of $ (4\times4)$-matrices.


$ \left(\begin{array}{cccc}\lambda_1 & 0 & 0 & 0\\ 0 & \lambda_2 & 0 & 0\\ 0 & 0 & \lambda_3 & 0 \\ 0 & 0 & 0 & \lambda_4\end{array}\right)$ $ \left(\begin{array}{cccc}\lambda_1 & 0 & 0 & 0\\ 0 & \lambda_1 & 0 & 0\\ 0 & 0 & \lambda_2 & 0 \\ 0 & 0 & 0 & \lambda_3\end{array}\right)$ $ \left(\begin{array}{cccc}\lambda_1 & 1 & 0 & 0\\ 0 & \lambda_1 & 0 & 0\\ 0 & 0 & \lambda_2 & 0 \\ 0 & 0 & 0 & \lambda_3\end{array}\right)$ $ \left(\begin{array}{cccc}\lambda_1 & 0 & 0 & 0\\ 0 & \lambda_1 & 0 & 0\\ 0 & 0 & \lambda_1 & 0 \\ 0 & 0 & 0 & \lambda_2\end{array}\right)$
$ \left(\begin{array}{cccc}\lambda_1 & 1 & 0 & 0\\ 0 & \lambda_1 & 0 & 0\\ 0 & 0 & \lambda_1 & 0 \\ 0 & 0 & 0 & \lambda_2\end{array}\right)$ $ \left(\begin{array}{cccc}\lambda_1 & 1 & 0 & 0\\ 0 & \lambda_1 & 1 & 0\\ 0 & 0 & \lambda_1 & 0 \\ 0 & 0 & 0 & \lambda_2\end{array}\right)$ $ \left(\begin{array}{cccc}\lambda_1 & 0 & 0 & 0\\ 0 & \lambda_1 & 0 & 0\\ 0 & 0 & \lambda_2 & 0 \\ 0 & 0 & 0 & \lambda_2\end{array}\right)$ $ \left(\begin{array}{cccc}\lambda_1 & 1 & 0 & 0\\ 0 & \lambda_1 & 0 & 0\\ 0 & 0 & \lambda_2 & 0 \\ 0 & 0 & 0 & \lambda_2\end{array}\right)$
$ \left(\begin{array}{cccc}\lambda_1 & 1 & 0 & 0\\ 0 & \lambda_1 & 0 & 0\\ 0 & 0 & \lambda_2 & 1 \\ 0 & 0 & 0 & \lambda_2\end{array}\right)$ $ \left(\begin{array}{cccc}\lambda_1 & 0 & 0 & 0\\ 0 & \lambda_1 & 0 & 0\\ 0 & 0 & \lambda_1 & 0 \\ 0 & 0 & 0 & \lambda_1\end{array}\right)$ $ \left(\begin{array}{cccc}\lambda_1 & 1 & 0 & 0\\ 0 & \lambda_1 & 0 & 0\\ 0 & 0 & \lambda_1 & 0 \\ 0 & 0 & 0 & \lambda_1\end{array}\right)$ $ \left(\begin{array}{cccc}\lambda_1 & 1 & 0 & 0\\ 0 & \lambda_1 & 1 & 0\\ 0 & 0 & \lambda_1 & 0 \\ 0 & 0 & 0 & \lambda_1\end{array}\right)$
$ \left(\begin{array}{cccc}\lambda_1 & 1 & 0 & 0\\ 0 & \lambda_1 & 0 & 0\\ 0 & 0 & \lambda_1 & 1 \\ 0 & 0 & 0 & \lambda_1\end{array}\right)$ $ \left(\begin{array}{cccc}\lambda_1 & 1 & 0 & 0\\ 0 & \lambda_1 & 1 & 0\\ 0 & 0 & \lambda_1 & 1 \\ 0 & 0 & 0 & \lambda_1\end{array}\right)$    

(Authors: Burkhardt/Höllig/Hörner)
  automatically generated 4/21/2005