1. The problem statement, all variables and given/known data Let V be an inner product space. For v ∈ V fixed, show that T(u) =< v, u > is a linear operator on V . 2. Relevant equations 3. The attempt at a solution First to show it is a linear operator, you show that T(u+g)=T(u)+T(g) and T(ku)=kT(u) So, T(u+g)=<v, u+g>=<v,u>+<v,g>=T(u)+T(g) Then T(ku)=<v, ku>=k<v,u> And since both the results are in the inner product space it is a linear operator on V? However, I don't know if this is right, because can't you not split up the second value like I did? Only the first? A little clarification would be appreciated! Thanks!