expressing class of inversions in einstein summation convention

Question

I'm working on a personal project where I'm studying the set of inversions in $\Bbb R^n$ that preserve the unit sphere centered at the origin; these transformations can be defined based on a center of inversion $c$, like so:

$$I_{c}(x) = (c\cdot c-1){{x-c}\over{(x-c)\cdot(x-c)}}+c$$

I'm curious about how this would be expressed in Einstein summation convention, but I'm not too familiar with it and my attempts have failed.

Answer 1

It would be$$[I_c(x)]_i=\frac{c_jc_j-1}{(x_k-c_k)(x_k-c_k)}(x_i-c_i)+c_i.$$