A pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but in three dimensions gains an additional sign flip under an improper rotation such as a reflection.
The cross product of two vectors is not a (true) vector, but rather a pseudovector. In reality the cross product is only defined in three dimensions. In all other dimension one must use the wedge product which results in a bivector.
In three dimensions, the dual of a bivector is a vector therefore the bivector (2-blade) is a pseudovector. In four dimensions, however, the dual of a trivector is a vector therefore trivectors are pseudovectors.
This page uses content from Wikipedia. The original article was at Pseudovector. The list of authors can be seen in the page history. As with the Math Wiki, the text of Wikipedia is available under the Creative Commons Licence. |
Community content is available under CC-BY-SA
unless otherwise noted.