Recent content by Sepen

Ah it would be Im(T) and it would be Im(T*) so thus they have to be equal?

I understand that but does that necessarily imply that they have to be equal? I recognize that they have to have the same dimensions in that case, but that doesn't get me anywhere.

Is that necessarily true? And if it is (I know that you can show that Im(T) is orthogonal to Ker(T*) and vice versa), but how does that specifically help?

Homework Statement Show that if T is a normal operator on a finite dimensional vector space than it has the same image as its adjoint. Homework Equations N/A The Attempt at a Solution I have been able to show that both T and T^{*} have the same kernel. Thus, by using the finite...