# Diagonalization and the Hadamard product

Let $$B \in \mathbb{C}^{n\times n}$$ be unitarily diagonalizable such that $$B=V\Lambda V^*$$. Let $$A=B\circ B$$ where $$\circ$$ accounts for the Hadamard product. Then we can say that $$A$$ is also unitarily diagonalizable. I need a hint for unitarily diagonalization of the matrix $$A$$ based on $$V$$ and $$\Lambda$$. Can we do that? At least can we get any information about the eigenvalues of $$A$$ based on eigenvalues of $$B$$?