Given a Block Matrix $ A \in \mathbb{R}^{\left( m + n \right) \times \left( m + n \right)} $:
$$ A = \begin{bmatrix} B & C \\ D & E \end{bmatrix} $$
Where $ B, E \in \mathbb{R}^{m \times m} $ and $ C, D \in \mathbb{R}^{n \times n} $
Let the SVD of $ A $ be given by $ A = U S {V}^{T} $.
Could one express the SVD of $ A $ by the SVD's of the Blocks? Namely by the SVD of $ B, C, D, E $?