3
$\begingroup$

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$$?

0 Answers 0