What Does Subtracting the Identity from a Transformation Mean in Nomenclature?

[pamparana]

Hello everyone,

I have a question about nomenclature and it may be a bit more than simple nomenclature as I am not quite sure I understand it:

So, I am reading a paper and going through it very slowly as it is quite intense. But one of the line is as follows:

Suppose the transformation s maps a point p to the point s(p). Let u = s - I be the displacement field associated with the transformation s.

I am confused as to what s - I represents. The subtracting of the identity from a transformation seems strange to me.

I always thought the displacement field can be simply represented for each particle by associating a vector with each particle...

I hope someone can clarify this doubt for me.

Many thanks,

Luc

 

[trambolin]

I guess, they try to describe the vector by saying the vector is defined by its starting point and end point $u = (x_2-x_1, y_2-y_1)$ and $s((x_1,y_1)) = (x_2,y_2)$.

They probably used the notation $(s-I)(p)$