Terminology
The term "reflection" is loose, and considered by some an abuse of language, with "inversion" preferred; however, "point reflection" is widely used. Such maps are involutions, meaning that they have order 2 – they are their own inverse: doing them twice yields the identity map – which is also true of other maps called "reflections". More narrowly, a "reflection" refers to a reflection in a hyperplane ( dimensional affine subspace – a point on the line, a line in the plane, a plane in 3-space), with the hyperplane being fixed, but more broadly "reflection" is applied to any involution of Euclidean space, and the fixed set (an affine space of dimension k, where ) is called the "mirror". In dimension 1 these coincide, as a point is a hyperplane in the line.
In terms of linear algebra, assuming the origin is fixed, involutions are exactly the diagonalizable maps with all eigenvalues either 1 or −1. Reflection in a hyperplane has a single −1 eigenvalue (and multiplicity on the 1 eigenvalue), while point reflection has only the −1 eigenvalue (with multiplicity n).
The term "inversion" should not be confused with inversive geometry, where "inversion" is defined with respect to a circle
Read more about this topic: Point Reflection