reflection

If we have a unit vector and a vector , we can reflect the vector by a plane perpendicular to .

This can be done by decomposing into the perpendicular component and the parallel component .

As Orthogonal Transformation

Both rotation and reflection are orthogonal transformation, and both of them preserve the origin and distance between two points. However, a key difference is that reflection does not preserve orientation.

When represented as an matrix , the reflection will have a determinant .

See Also

• two reflections give a rotation