# Generic name for the operator $L = (I + \alpha U V)$

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 ?

• 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" – Jean Marie Aug 13 at 11:42
• Thanks. That helps! – Mathnoob Aug 13 at 11:51
• It also is a special case of the Schur Complement. – user617446 Aug 13 at 12:25