improper rotation in a sentence

Examples

1. 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 rotation matrix " R ", so that a position vector "'x "'is transformed to.
2. 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 rotation matrix " R ", so that a position vector "'x "'is transformed to.