Suppose we have a matrix A. We have decomposed A into a sum of the identity matrix and the product of two column(G) and row(H) matrices.
In general, how can we calculate $A^{-1}$?
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Zeta.Investigator
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This question might help you. But I'm not certain. – Eff Oct 17 '15 at 19:35
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The Woodbury Matrix Idendity may help you as well. – Eff Oct 17 '15 at 19:41
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@Eff More like Sherman–Morrison formula. Thanks;) – Zeta.Investigator Oct 17 '15 at 19:48
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I believe you may be describing a rank one update to the identity matrix. This has been discussed in a number of previous Questions, such as Rank one perturbation proof. – hardmath Oct 17 '15 at 19:50
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@hardmath Seems like they are the same. But the thing is I didn't quite know "Rand one perturbation" has anything to do with my question beforehand... – Zeta.Investigator Oct 17 '15 at 20:02
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We are all here to learn! It's a good question, just one that (in part disguised by non-obvious terminology) has come up before. Note that if either $G=0$ or $H=0$, the "update" just gives us the identity matrix again. – hardmath Oct 17 '15 at 20:06