In physics and mathematics , a pseudovector ( or axial vector ) is a quantity that transforms like a vector under a proper rotation , but gains an additional sign flip under an improper rotation ( a transformation that can be expressed as an inversion followed by a proper rotation ) . In physics and mathematics , a pseudovector ( or axial vector ) is a quantity that transforms like a vector under a proper rotation , but gains an additional sign flip under an improper rotation such as a reflection .