M = matrix([[4,-1,6],[2,1,6],[2,-1,8]])
MM=M.jordan_form(transformation=true)
show(MM)
show(MM[0])
show(MM[1])
show(MM[1]^(-1))
show(MM[1]^(-1)*MM[1])
show(MM[1]^(-1)*MM[0]*MM[1])
show(bool(MM[1]^(-1)*MM[0]*MM[1]==M))According to the documentation and what I know of Jordan decomposition the last line should be True. No ?
Jordan canonical form is given by J = T^{-1} A T
A = matrix([[4,-1,6],[2,1,6],[2,-1,8]])
J, T = A.jordan_form(transformation=True)
T^(-1)*(A * T) == J
TrueYou checked:
T^(-1)*J*T == Awhich is not the same
Note that
T*J*T^(-1) == A
TrueOk but my formula is in the quickref-linalg.pdf . Someone should modify it.
And I wonder what arr the matrix obtained by my way.
The matrix P from quickref-linalg.pdf is inverse to the transformation T. Your MM[1] corresponds to P
Asked: 2 years ago
Seen: 146 times
Last updated: Jan 28 '23
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