How to find the pseudo-inverse of the following block lower triangular matrix? $$X=\begin{bmatrix} A & 0 \\ c & d \\ \end{bmatrix}$$ Where $A$ is a $n\times n$ lower triangular matrix, $d$ is a scalar and $c$ is a $1\times n$ vector. Suppose that I know inverse of $A$ a priori.
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2If $A$ is assumed to be invertible and $d$ is non-zero, then the pseudo-inverse is just its inverse. You can refer to this article "SINGULAR VALUE DECOMPOSITION AND THE MOORE-PENROSE INVERSE OF BORDERED MATRICES by ROBERT E. HARTWIG" for some pseudo-inverse formulas of such matrices. – La Rias Mar 08 '16 at 05:35
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@La Rias: great reference. https://www.jstor.org/stable/2100398?seq=1#page_scan_tab_contents – dantopa Mar 29 '17 at 15:43
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A related question. – J. M. ain't a mathematician Mar 08 '19 at 10:17