Define T in L(C2) by T(w,z)=(−z,w).
Find the generalized eigenspaces corresponding to the distinct eigenvalues of T.
I believe that once I have the eigenvalues, I know how to find the eigenspaces, but I'm not sure I'm looking for the eigenvalues correctly.
I know that if the eigenvalues are a,b corresponding to (w,0) and (0,z) respectively, then (ab)=1, since a(w)=−z implies ab(−z)=−z. But I think my whole approach to this is wrong and that I'm missing some very elementary idea.