---
tag: 57BM2XNEK4
kind: concept
name: Rotor (mathematics)
sources:
  - wikipedia: en:9807828@r1356547685
    locator: Rotor (mathematics)
    note: adopted
    mention: wikipedia://en/9807828
    sections: [Summary]
same_as:
  wikidata: Q7370585
  wikipedia: Rotor (mathematics)
inventory: [YMD10EM73G]
---

## Summary

A **rotor** is an object in the geometric algebra (also called Clifford algebra) of a [[vector space|000AYPA9AJ]] that represents a [[rotation|0HFREYRSZP]] about the origin. More precisely, for each rotation there exist two rotors that represent it. The term originated with William Kingdon Clifford, in showing that the [[quaternion|0GE4DVQKR8]] algebra is just a special case of Hermann Grassmann's "theory of extension" (Ausdehnungslehre). Hestenes defined a rotor to be any element $R$ of a geometric algebra that can be written as the product of an even number of unit vectors and satisfies $R\tilde R = 1$, where $\tilde R$ is the "reverse" of $R$—that is, the product of the same vectors, but in reverse order.