Proving Convexity of Numerical Range for Normal T

[julydecember]

Homework Statement

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.

Homework Equations

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?

 

[quasar987]

Homework Statement

If T is a linear transformation on the finite-dimensional inner product space over complex numbers

which finite-dimensional inner product space? And what is the codomain of T?

and is normal,

what does normal mean?

then prove that the numerical range of T is convex.

Do you mean "prove that the image of T is convex"?