1.17 Compute the Jordan canonical/normal form of a matrix A

Mathematica

Remove["Global`*"]; m={{3,-1,1,1,0,0}, {1, 1,-1,-1,0,0}, {0,0,2,0,1,1}, {0,0,0,2,-1,-1}, {0,0,0,0,1,1}, {0,0,0,0,1,1}}; MatrixForm[m]	$$\left(\begin{array}{cccccc}3& -1& 1& 1& 0& 0\\ 1& 1& -1& -1& 0& 0\\ 0& 0& 2& 0& 1& 1\\ 0& 0& 0& 2& -1& -1\\ 0& 0& 0& 0& 1& 1\\ 0& 0& 0& 0& 1& 1\end{array}\right)$$
{a,b}=JordanDecomposition[m]; b	$$\left(\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 2& 1& 0& 0& 0\\ 0& 0& 2& 0& 0& 0\\ 0& 0& 0& 2& 1& 0\\ 0& 0& 0& 0& 2& 1\\ 0& 0& 0& 0& 0& 2\end{array}\right)$$

 

Matlab

clear all; A=[3 -1 1 1 0 0; 1 1 -1 -1 0 0; 0 0 2 0 1 1; 0 0 0 2 -1 -1; 0 0 0 0 1 1; 0 0 0 0 1 1;] jordan(A)

ans = 0 0 0 0 0 0 0 2 1 0 0 0 0 0 2 1 0 0 0 0 0 2 0 0 0 0 0 0 2 1 0 0 0 0 0 2

 

Maple

restart; A:=Matrix([[3,-1,1,1,0,0], [1, 1,-1,-1,0,0], [0,0,2,0,1,1], [0,0,0,2,-1,-1], [0,0,0,0,1,1], [0,0,0,0,1,1]]); LinearAlgebra:-JordanForm(A);

$$\left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\\ 0& 2& 1& 0& 0& 0\\ 0& 0& 2& 1& 0& 0\\ 0& 0& 0& 2& 0& 0\\ 0& 0& 0& 0& 2& 1\\ 0& 0& 0& 0& 0& 2\end{array}\right]$$