Reflection through the origin

Inversion with respect to the origin

In mathematics, reflection through the origin refers to the point reflection of Euclidean spaceR across the origin of the Cartesian coordinate system. Reflection through the origin is an orthogonal transformation corresponding to scalar multiplication by ${\displaystyle -1}$, and can also be written as ${\displaystyle -I}$, where ${\displaystyle I}$ is the identity matrix. In three dimensions, this sends ${\displaystyle (x,y,z)\mapsto (-x,-y,-z)}$, and so forth.