What is "pseudotensor"

n. (context mathematics physics English) A quantity that transforms like a tensor under a proper rotation but gains an additional change of sign under an improper rotation.

In physics and mathematics, a pseudotensor is usually a quantity that transforms like a tensor under an orientation-preserving coordinate transformation (e.g., a proper rotation), but additionally changes sign under an orientation reversing coordinate transformation (e.g., an improper rotation, which is a transformation that can be expressed as a proper rotation followed by reflection). In this sense, it is a generalization of a pseudovector.

There is a second meaning for pseudotensor, restricted to general relativity; tensors obey strict transformation laws, but pseudotensors are not so constrained. Consequently, the form of a pseudotensor will, in general, change as the frame of reference is altered. An equation containing pseudotensors which holds in one frame will not necessarily hold in a different frame; this makes pseudotensors of limited relevance because equations in which they appear are not invariant in form.