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# Pseudovector

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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).^{[1]}

## Physical examples

Physical examples of pseudovectors include the magnetic field, torque, vorticity, and the angular momentum.^{[2]}

## References

- ↑ A simple example of an improper rotation in 3D (but not in 2D) is a coordinate inversion:
**x**goes to −**x**,**y**to −**y**and**z**to −**z**. Under this transformation,**a**and**b**go to −**a**and −**b**(by the definition of a vector), but**p**clearly does not change. It follows that any improper rotation multiplies**p**by −1 compared to the rotation's effect on a true vector. - ↑ Often, the distinction between vectors and pseudovectors is overlooked, but it becomes important in understanding and exploiting the effect of symmetry on the solution to physical systems.

- George B. Arfken and Hans J. Weber,
*Mathematical Methods for Physicists*(Harcourt: San Diego, 2001). (ISBN 0-12-059815-9) - John David Jackson,
*Classical Electrodynamics*(Wiley: New York, 1999). (ISBN 0-471-30932-X) - Susan M. Lea, "Mathematics for Physicists" (Thompson: Belmont, 2004) (ISBN 0-534-37997-4)