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Specifying "full rank" to "full column rank", since the matrix does not need to have full row rank for the following equation to hold |
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This computation of the pseudoinverse requires (''n'' + ''p'')-square matrix inversion and does not take advantage of the block form.
To reduce computational costs to ''n''- and ''p''-square matrix inversions and to introduce parallelism, treating the blocks separately, one derives <ref name=Baksalary>{{cite journal|author=[[Jerzy Baksalary|J.K. Baksalary]] and O.M. Baksalary|title=Particular formulae for the Moore–Penrose inverse of a columnwise partitioned matrix|journal=Linear Algebra Appl.|volume=421|date=2007|pages=16–23|doi=10.1016/j.laa.2006.03.031|doi-access=
:<math>\begin{align}
\begin{bmatrix}\mathbf A & \mathbf B\end{bmatrix}^+ &=
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