Is there any interesting geometric (or any of kind) characteristic of a transformation T of a vector X in $R^n$ so that the components get squared? i.e. $T(x_1,x_2,...,x_n)=(x_1^2, x_2^2,..., x_n^2)$ for any $X= (x_1,x_2,...,x_n)$ in $R^n$.
I'm especially looking for a geometric relation between the vectors before and after the transformation.