# Pseudovector

In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but gains an additional sign flip under an improper rotation such as a reflection. Geometrically it is the opposite, of equal magnitude but in the opposite direction, of its mirror image. This is as opposed to a true or polar vector (more formally, a contravariant vector), which on reflection matches its mirror image.

In three dimensions the pseudovector p is associated with the cross product of two polar vectors a and b:

The vector p calculated this way is a pseudovector. One example is the normal to an oriented plane. An oriented plane can be defined by two non-parallel vectors, a and b, which can be said to span the plane. The vector a × b is a normal to the plane (there are two normals, one on each side – the right-hand rule will determine which), and is a pseudovector. This has consequences in computer graphics where it has to be considered when transforming surface normals.

A number of quantities in physics behave as pseudovectors rather than polar vectors, including magnetic field and angular velocity. In mathematics pseudovectors are equivalent to three dimensional bivectors, from which the transformation rules of pseudovectors can be derived. More generally in n-dimensional geometric algebra pseudovectors are the elements of the algebra with dimension n − 1, written Λn−1Rn. The label 'pseudo' can be further generalized to pseudoscalars and pseudotensors, both of which gain an extra sign flip under improper rotations compared to a true scalar or tensor.

Read more about Pseudovector:  Physical Examples, Details, The Right-hand Rule, Geometric Algebra

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Scalar Triple Product - Scalar or Pseudoscalar
... product of two vectors is a scalar but the dot product of a pseudovector and a vector is a pseudoscalar, so the scalar triple product must be pseudoscalar valued ...
Vector Meson
... Compare to a pseudovector meson, which has a total spin 1 and even parity ... only slightly realized among the tensor meson and pseudovector meson multiplets ... Pseudovector mesons transition by a similar process into pseudoscalar mesons ...
Pseudovector Meson
... In high energy physics, a pseudovector meson or axial vector meson is a meson with total spin 1 and even parity (usually noted as JP=1+) ... The known pseudovector, or axial vector, mesons fall into two different classes those with JPC=1+-, and those with JPC=1++ ... There are considerable experimental uncertainties in pseudovector meson masses which will require additional experimental data to clarify ...
Cross Product and Handedness
... is not fixed a priori, the result is not a (true) vector but a pseudovector ... Therefore, for consistency, the other side must also be a pseudovector ... a cross product may be either a vector or a pseudovector, depending on the type of its operands (vectors or pseudovectors) ...
Pseudovector - Geometric Algebra - Note On Usage
... all authors in the field of geometric algebra use the term pseudovector, and some authors follow the terminology that does not distinguish between the pseudovector and the cross ... generalize beyond three dimensions, the notion of pseudovector based upon the cross product also cannot be extended to higher dimensions ... The pseudovector as the (n–1)-blade of an n-dimensional space is not so restricted ...