2020-09-01 14:20:12 +0200 received badge ● Scholar (source) 2020-09-01 14:20:10 +0200 commented answer Two methods that return different eigenspaces Thank you, that answers my question! I don't see the point of using vertices=list(J)... 2020-08-30 19:31:10 +0200 asked a question Two methods that return different eigenspaces 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]) ]