I need to find a conjugacy between these matrices. I first checked that they are similar (characteristic polynomial is same) and I get +-2i as eigenvalues. But our book does not go over a process of actually finding this conjugacy. The fact that the eigenvectors/eigenvalues are complex just makes me more confused.
I know the eigenvectors for both matrices and thus can find the matrix that will break each A, B down to canonical form, I'm just stuck from there.
Conceptually, I know that we can find a conjugacy from one canonical form to another, and then apply the transformation matrices from A, B back to this conjugacy to get the final answer, but I don't know the actual computations/rules.
Thanks!