I don't understand why eigenspaces() and adjacency_matrix().eigenspaces_right() return different results (see the example below). If I understand the reference manual correctly, that shouldn't be the case.
> J = graphs.JohnsonGraph(5,2)
> J.eigenspaces()
[
(6, Vector space of degree 10 and dimension 1 over Rational Field
User basis matrix:
[1 1 1 1 1 1 1 1 1 1]),
(1, Vector space of degree 10 and dimension 4 over Rational Field
User basis matrix:
[ 1 0 0 0 1/2 1/2 0 -1/2 -1/2 -1]
[ 0 1 0 0 -3/2 -1/2 1 -1/2 -1/2 1]
[ 0 0 1 0 -1 -1 1 -1 0 1]
[ 0 0 0 1 1/2 -1/2 -1 1/2 -1/2 0]),
(-2, Vector space of degree 10 and dimension 5 over Rational Field
User basis matrix:
[ 1 0 0 0 -1 0 -1 0 1 0]
[ 0 1 0 0 0 0 -1 -1 1 0]
[ 0 0 1 0 -1 0 0 1 0 -1]
[ 0 0 0 1 -1 0 0 0 1 -1]
[ 0 0 0 0 0 1 -1 -1 0 1])
]
and
> J = graphs.JohnsonGraph(5,2)
> J.adjacency_matrix().eigenspaces_right()
[
(6, Vector space of degree 10 and dimension 1 over Rational Field
User basis matrix:
[1 1 1 1 1 1 1 1 1 1]),
(1, Vector space of degree 10 and dimension 4 over Rational Field
User basis matrix:
[ 1 0 0 0 -1 -1/2 1/2 1/2 0 -1/2]
[ 0 1 0 0 0 1/2 -1/2 1/2 -1 -1/2]
[ 0 0 1 0 1 -1/2 -1/2 -3/2 1 -1/2]
[ 0 0 0 1 1 -1 -1 -1 1 0]),
(-2, Vector space of degree 10 and dimension 5 over Rational Field
User basis matrix:
[ 1 0 0 0 0 0 0 -1 -1 1]
[ 0 1 0 0 0 -1 1 -1 -1 1]
[ 0 0 1 0 0 -1 0 0 -1 1]
[ 0 0 0 1 0 0 1 -1 -1 0]
[ 0 0 0 0 1 -1 1 0 -1 0])
]
