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## 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?

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