The discussion so far only relates to proper rotations, i.e. rotations about an axis. However, one can also consider improper rotations, i.e. a mirror-reflection possibly followed by a proper rotation. (One example of an improper rotation is inversion through a point in 3-dimensional space.) Suppose everything in the universe undergoes an improper rotation described by the improper rotation matrix "R", so that a position vector x is transformed to . If the vector v is a polar vector, it will be transformed to . If it is a pseudovector, it will be transformed to .