- #1
nautolian
- 34
- 0
Homework Statement
Let V be an inner product space. For v ∈ V fixed, show
that T(u) =< v, u > is a linear operator on V .
Homework Equations
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!