Given a block partitioned matrix $\boldsymbol{A}$
$$ \boldsymbol{A} = \begin{bmatrix} \boldsymbol{A}_{1,1} & \boldsymbol{A}_{1,2} & \cdots \\ \boldsymbol{A}_{2,1} & \boldsymbol{A}_{2,2} & \cdots \\ \vdots & \vdots \end{bmatrix}, $$
what can be said about its SVD decomposition in terms of its constituting blocks $\boldsymbol{A}_{i,j}$?