Pseudotensor

Definition

In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under an orientation-preserving coordinate transformation but additionally changes sign under an orientation-reversing coordinate transformation, which is a transformation that can be expressed as a proper rotation followed by reflection. This is a generalization of a pseudovector. To evaluate a tensor or pseudotensor sign, it has to be contracted with some vectors, as many as its rank is, belonging to the space where the rotation is made while keeping the tensor coordinates unaffected. Under improper rotation a pseudotensor and a proper tensor of the same rank will have different sign which depends on the rank being even or odd. Sometimes inversion of the axes is used as an example of an improper rotation to see the behaviour of a pseudotensor, but it works only if vector space dimensions is odd otherwise inversion is a proper rotation without an additional reflection.

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