Can a Hermitian Matrix be Decomposed into a Sum of Unitary Matricies?

Question

Given a Hermitian matrix $A$, when is it possible to write $A$ as a sum of unitary matricies as in the following form?

$$ A = \sum_{i} a_i U$$

Where $U$ is unitary.

Intuitively, because you have a nice SVD: $A = U \Sigma U^{\dagger}$, I would expect to see that this is always possible with the coefficients somehow related to the eigenvalues, but I am not entirely sure.

Answer 1

I was too restrictive when I wrote this question and missed this result: Every matrix can be written as a sum of unitary matrices? Turns out every complex square matrix can be written as a linear sum of at most two unitary matricies.