A=matrix(5,5,[2,0,4,1,3,0,1,0,5,1,0,5,1,3,3,0,0,0,1,0,0,0,0,-1,3])
print A.charpoly().factor()
print A.eigenvalues()
E=identity_matrix(5)
print (A-E).rank()
print (A-2*E).rank()
print (A-3*E).rank()
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(x - 3) * (x - 2) * (x - 1)^3
[3, 2, 1, 1, 1]
4
4
4
(x - 3) * (x - 2) * (x - 1)^3
[3, 2, 1, 1, 1]
4
4
4
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