Hi:
Something funny is going on:
sage: MS = MatrixSpace(CC, 2, 2)
sage: A = MS([[1,5],[3,-1]])
sage: A.eigenspaces()
[
(4.00, [
(1.00, 1.00)
]),
(-4.00, [
])
]
sage: A.eigenspaces()[0]
(4.00, [
(1.00, 1.00)
])
Hello all:
In trying to compute the eigenvalues and eigenvectors of the
discrete Fourier transformation for Z/5Z for a class I'm teaching,
I came across the following:
sage: MS = MatrixSpace(CyclotomicField(5),5,5)
sage: z = CyclotomicField(5).gen()
sage: F5 =
MS([[1,1,1,1,1],[1,z,z^2,z^3,z^4],
