A common way of constructing a pseudovector **p** is by taking the cross product of two vectors **a** and **b**:

This concept can be further generalized to **pseudoscalars** and **pseudotensors**, both of which gain an extra sign flip under improper rotations compared to a true scalar or tensor.

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. For example, consider the case of an electrical current loop in the *z*=0 plane: this system is symmetric (invariant) under mirror reflections through the plane (an improper rotation), but the magnetic field is anti-symmetric (flips sign) under that mirror plane—this contradiction is resolved by realizing that the mirror reflection of the field induces an extra sign flip because of its pseudovector nature.

To the extent that physical laws are the same for right-handed and left-handed coordinate systems (i.e. invariant under inversion), the sum of a vector and a pseudovector is not meaningful. However, the weak nuclear force that governs beta decay *does* depend on the handedness of the universe, and in this case pseudovectors and vectors *are* added.

- George B. Arfken and Hans J. Weber,
*Mathematical Methods for Physicists*(Harcourt: San Diego, 2001). - John David Jackson,
*Classical Electrodynamics*(Wiley: New York, 1999).