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2.46.5  Jordan normal form : jordan

jordan takes as argument a square matrix A of size n.
jordan returns :

Remarks

Input in Xcas, Mupad or TI mode :

jordan([[1,0,0],[0,1,1],[1,1,-1]])

Output :

[[1,0,0],[0,1,1],[1,1,-1]],[[-1,0,0],[1,1,1],[0,-sqrt(2)-1,sqrt(2)-1]],[[1,0,0],[0,-(sqrt(2)),0],[0,0,sqrt(2)]]

Input in Maple mode :

jordan([[1,0,0],[0,1,1],[1,1,-1]])

Output :

[[1,0,0],[0,-(sqrt(2)),0],[0,0,sqrt(2)]]

then input :

P)

Output :

[[-1,0,0],[1,1,1],[0,-sqrt(2)-1,sqrt(2)-1]]

Input in Xcas, Mupad or TI mode :

jordan([[4,1,-2],[1,2,-1],[2,1,0]])

Output :

[[[1,2,1],[0,1,0],[1,2,0]],[[2,1,0],[0,2,1],[0,0,2]]]

In complex mode and in Xcas, Mupad or TI mode , input :

jordan([[2,0,0],[0,2,-1],[2,1,2]])

Output :

[[1,0,0],[-2,-1,-1],[0,-i,i]],[[2,0,0],[0,2-i,0],[0,0,2+i]]

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