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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


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

© 1996-9 Eric W. Weisstein