Let $A$ be a positive matrix, may not be invertible. I define its generalised inverse as \begin{equation} A^- = \lim_{n\rightarrow \infty} \left( \frac{1}{n} I + A\right)^{-1}. \end{equation} Lets consider a strictly positive matrix $B$ (which by definition, is invertible). Is it true that \begin{equation} (BAB)^- = B^{-1}A^- B^{-1}. \end{equation} Advanced thanks for any helps and suggestions.
2026-04-07 12:54:13.1775566453
On generalised inverse
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