Consider $$\mathbf{A,B}$$ two matrices which are unitary and/or Hermitian, What can we say about eigenvalues of their Hadamard product $$(\mathbf{A \circ B})$$?

Can we bound the eigenvalues in relation to normal matrix product $$(\mathbf{AB})$$

Thanks!

• I think Horn and Johnson mention something about this in Matrix Analysis – Santana Afton Mar 14 at 15:13
• @SantanaAfton Can you point it out, I couldn't find any related result. – Astro Mar 14 at 15:42