One can use the following command to find the Jordan form of a square matrix \(A\) in SageMath:
A.jordan_form(transformation=True)
Section 8.3 Examples
Activity 8.3.1. Computing Jordan Canonical Forms.
In this activity, we’ll practice finding the Jordan canonical form of different matrices using both theoretical understanding and computational tools.
(a) Jordan Form of a 5×5 Matrix.
Find the Jordan canonical form of the matrix
\begin{equation*}
A = \begin{pmatrix}
-1 \amp 0 \amp 0 \amp 0 \amp -9 \\
0 \amp 2 \amp 0 \amp 0 \amp 1 \\
0 \amp 0 \amp 2 \amp 0 \amp 0 \\
0 \amp 0 \amp 1 \amp 2 \amp 0 \\
1 \amp 0 \amp 0 \amp 0 \amp 5
\end{pmatrix}
\end{equation*}
Checkpoint 8.3.1. Practice Problems.
Find the Jordan canonical form of the following matrices:
-
\(\displaystyle A = \begin{pmatrix} 11 \amp -4 \amp -5 \\ 21 \amp -8 \amp -11 \\ 3 \amp -1 \amp 0 \end{pmatrix}\)
-
\(\displaystyle B = \begin{pmatrix} 2 \amp 1 \amp 0 \amp 0 \\ 0 \amp 2 \amp 1 \amp 0 \\ 0 \amp 0 \amp 3 \amp 0 \\ 0 \amp 1 \amp -1 \amp 3 \end{pmatrix}\)
