I have to prove that the eigenspace, E lambda is an invariant subspace.
I took some eigenvector, v in the eigenspace, then T(v) =lambda v
I know that T(v) should belong to the eigenspace , but i don't really understand why ?
Elambda is the set of all eigenvectors of T, then why would (lambda) (v) be in the eigenspace ?
I am confused.