If there is a symmetric matrix, say
$B = \left[\begin{array}{cc} 0 & A\\ A^T & 0 \end{array}\right]$
where $A$ is a $m\times n$ submatrix with $m \geq n$.
Is it possible to express the eigenvalues and eigenvectors of $B$, in terms of singular values and singular vectors of $A$?
(Apologies for the bad formatting)