Pseudotensor

A Tensor-like object which reverses sign under inversion. Given a transformation Matrix ${\hbox{\sf A}}$,

$${A_{ij}}' = \mathop{\rm det}\vert\,{\hbox{\sf A}}\vert a_{ik}a_{jl}A_{kl},$$

where det is the Determinant. A pseudotensor is sometimes also called a Tensor Density.

See also Pseudoscalar, Pseudovector, Scalar, Tensor Density

References

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