What is the theory behind elementary matrices?

[stanley.st]

Hello,

I need to find some theory about elementary matrices. That are the matrices in the form

$$\mathbf{E}(\sigma,\mathbf{u},\mathbf{v})=\mathbf{I}-\frac{1}{\sigma}\mathbf{uv}^{T}$$

I can't find anywhere some theory about it. Can you give me some useful links?

Thank you so much...

 

[tiny-tim]

Hello stanley.st!

If you can't find a link, where did you come across this?

(it's not something I've seen before)

 

[Werg22]

Any decent linear algebra book covers elementary matrices.