Given an $m\times n$ matrix $A$, where $m<n$, can the expression $(AA^T)^{-1}A$ be simplified?
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@SamStreeter Is there a formula for the inverse of the product of non-square matrices? – Museful Nov 08 '18 at 09:42
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1Short answer: no. – egreg Nov 08 '18 at 09:54
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$(AA^T)^{-1}A$ is the Moore–Penrose inverse of $A^T$. The expression cannot be simplified in general.
lhf
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In general no, but you could express it in different terms. One instance of what I say is QR decomposition, so doing the decomposition for $A^T$ $$A^T = QR$$ You will get $$(AA^T)^{-1}A = (R^TQ^TQR)^{-1}R^TQ^T = (R^TR)^{-1}R^TQ^T$$
Ahmad Bazzi
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