I am given a symmetric positive semi-definite matrix $A\in\mathbb{R}^{n\times n}$. I perform the SVD, $$A = V \Sigma V^\top,$$ where $V$ is unitary and $\Sigma$ is diagonal. Next, I pick up another positive semi-definite diagonal matrix $\Xi$ and construct $$B = V\Xi V^\top.$$ I.e., the matrices $A$ and $B$ have the same eigenvectors but different eigenvalues.
Is there any name for this relation? Hopefully, any nice properties for $A$ and $B$?