Hi, I am trying to prove the following equality
Range(T*T) = Range(T*)
where T is a linear transformation and * denotes the adjoint.
I know I must first show that Range(T*T) Range(T*) and vice versa.
so, Let w exist in R(T*T), then there exists a v in vector space V s.t.
T*T(v) = w.
Then I draw a blank, what's next??? Or am I even starting it correctly?