What is the meaning of "values coincides with the convex closure of the eigenvalues"?

Question

In this paper, it says.

What is the meaning of the sentence,

"F(M) coincides with the convex closure of the eigenvalues if M is normal."

I understand what is a normal matrix.

But what does it mean to have values which 'coincides with the convex closure of the eigenvalues".

Answer 1

If $c_1,c_2,...,c_n$ are the eigen values then the convex closure of eigen values is the set of numbers of the form $\sum a_ic_i$ where $a_i \geq 0$ and $\sum a_i=1$.