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