I'm trying to compute eigenvalues and eigenvectors for certain matrices. Most of the time sage is giving me what seems to be the correct output, but sometimes it's quite wrong and I'm not sure why this is happening. Here's a concrete example with a circulant matrix.
sage: M=matrix.circulant([1,-1/2*I,0,0,0,0,0,0,0,0,1/2*I])
sage: M.eigenvectors_right()
[(1, [(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1)], 1)]
That is, it only returns a single eigenvector when I know there's in fact 11. A different issue appears with matrix.circulant([1,-1/2I,0,0,0,0,1/2I]), where now sage produces all the eigenvalues but produces no eigenvectors for most of these values.
