Is it possible to say anything about the eigenvalues and eigenvectors of a matrix
$X = Y \circ xx^T$
where $Y$ is a positive definite symmetric matrix with known eigen-decomposition
and $x$ is a vector. In particular if
what is the relationship between $V,U$ and $\Lambda, \Phi$. And/or is there an $O(n^2)$ to compute $V,\Phi$ from $U,\Lambda$ where $n$ is the size of the matrices.