# Pseudovector **A quantity which does not transform under reflections like a [[vector]] but otherwise behaves like one under rotations and translations.** ![[Pseudovector.svg|500]] *The [[cross product]] of two vectors is a pseudovector because reflecting the system causes the cross product to reverse in direction* A *psuedovector* is a quantity which, like a vector, is described and expressed by both a magnitude and direction and behave the same when rotated and translated, but *does not* behave like a vector when *reflected*. ## Definition In physics, the definition of a vector includes the requirement that it consists of components which all rotate with a rotation of the system. If a rotation is described by the rotation [[matrix]] $R$ and there is a position vector $\mathbf{r}$ such that $\mathbf{r}'=R\mathbf{r}$, then a vector $\mathbf{v}$ must also satisfy the equation $\mathbf{v}'=R\mathbf{v}$. Such a vector is also known as a *polar vector*. Polar vectors also satisfy the equations for improper rotations, reflections which may or may not be combined with a rotation. > [!NOTE] Psuedovector > A *pseudovector* $\mathbf{v}$ is a quantity with magnitude and direction which, when transformed by an improper rotation described by matrix $R$ into $\mathbf{v}'$, satisfies the equation > $\mathbf{v}'=-R\mathbf{v}$ > That is, it reverses direction when reflected.