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I would like to know if there is a general name for the operator $ L = (I + \alpha U V)$. I encounter this in the Householder reflection, with $\alpha = -1$ and $V = U^T$, therefore $H = (I - U U^T)$.

In general, $U$ and $V$ are vectors of the same dimension.

But in general does the above mentioned general operator $L$ have any specific names ?

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    $\begingroup$ I don't think there is a general name for this kind of matrix. If you are looking for keywords for a web search, try "perturbation of a matrix by a rank-one matrix" $\endgroup$ – Jean Marie Aug 13 at 11:42
  • $\begingroup$ Thanks. That helps! $\endgroup$ – Mathnoob Aug 13 at 11:51
  • $\begingroup$ It also is a special case of the Schur Complement. $\endgroup$ – user617446 Aug 13 at 12:25

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