1. The problem statement, all variables and given/known data If T is a linear transformation on the finite-dimensional inner product space over complex numbers and is normal, then prove that the numerical range of T is convex. 2. Relevant equations 3. The attempt at a solution If we assume a and b are in the numerical range of T, then we have to prove that (1-c)a + c b is also in the numerical range of T for 0<= c <= 1. Can someone give some help, please?