Given a $nm \times m$ matrix $A = \begin{pmatrix} A_1 \\ A_2 \\ \vdots \\ A_n\end{pmatrix}$ over $\mathbb{C}$, where $A_i$'s are $m \times m$ and $rank(A) = m$, is there an expression for the pseudo-inverse of $A$ in terms of the pseudo-inverses or SVDs of $A_i$'s? The $A_i$'s are not generally full-rank.
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$\begingroup$ I don't think there is much more to say than you can read on en.wikipedia.org/wiki/Block_matrix_pseudoinverse $\endgroup$Carlo Beenakker– Carlo Beenakker2019-08-28 10:32:59 +00:00Commented Aug 28, 2019 at 10:32
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$\begingroup$ Thank you for your reply but the partitioning seems to be different. In this case, I am partitioning over the larger dimension as opposed to the smaller dimension in the Wikipedia article. As such, I don't think the results transfer over. $\endgroup$Jinhui Wang– Jinhui Wang2019-08-29 21:40:34 +00:00Commented Aug 29, 2019 at 21:40
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