Pseudoscalar

A Scalar which reverses sign under inversion is called a pseudoscalar. The Scalar Triple Product

$${\bf A}\cdot ({\bf B}\times {\bf C})$$

is a pseudoscalar. Given a transformation Matrix ${\hbox{\sf A}}$,

$$S' = \mathop{\rm det}\vert{\hbox{\sf A}}\vert S,$$

where det is the Determinant.

See also Pseudotensor, Pseudovector, Scalar

References

Arfken, G. ``Pseudotensors, Dual Tensors.'' §3.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 128-137, 1985.