1. The problem statement, all variables and given/known data T is a linear operator on a finite dimensional vector space. then N(T*T)=N(T). the null space are equal. 2. Relevant equations 3. The attempt at a solution this is my method, but its does not work if dim(R(T))=0. i'm only concerned with showing N(T*T) [tex]\subseteq[/tex] N(T). let x beong to N(T*T) then <T*T(x),y>=0=<T(x),T(y)> for all y in the vector space. thus, if dim(R(T)) > 0 then there exists y such that T(y) is not equal to zero so T(x)=0. any other methods out there?