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);

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