Positive non self adjoint operator?

[broncos#1]

Homework Statement

Find an operator T on F^2 such that <T(v),v> is greater than or equal to 0 for all v in F^2, but T is not self-adjoint

Homework Equations

The Attempt at a Solution

I am trying to to find examples where <T(v),v>=0 where the operator is not 0

 

[Dick]

Think about rotations.

 

[Hurkyl]

I am trying to to find examples where <T(v),v>=0 where the operator is not 0

Can't you use algebra to solve for all possible values of T?