# Antivector

An **antivector** is an element of grade *n* − 1 in an *n*-dimensional exterior algebra.^{[1]} An antivector is always a blade, and it gets its name from the fact that its components each involve a combination of all except one basis vector, thus being the opposite of a vector whose components each involve exactly one basis vector. Like a vector, an antivector has *n* components in *n*-dimensional space, and this sometimes leads to an inadequate distinction being made between the two types of entities. However, antivectors transform differently with a change of basis than vectors do, which shows that they are different kinds of quantities.
In physics, the names *pseudovector* and *axial vector* are used to describe vectors that transform in the same way that an antivector transforms. These typically arise as the result of cross products between two vectors.

## See also

## References

- ↑ Lengyel, Eric (2016).
*Foundations of Game Engine Development, Volume 1: Mathematics*. Terathon Software LLC. ISBN 978-0-9858117-4-7.

Original source: https://en.wikipedia.org/wiki/Antivector.
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