# Quaternion

A quaternion is a member of a four-dimensional noncommutative division algebra (i.e., a ring in which every nonzero element has a multiplicative inverse, but multiplication is not necessarily commutative) over the real numbers.

Quaternion is a college-level concept that would be first encountered in an abstract algebra course covering rings and fields.

### Prerequisites

Commutative: | An operation * is said to be commutative if x*y = y*x for all x and y. |

Complex Number: | A complex number is a number consisting of a real part and an imaginary part. A complex number is an element of the complex plane. |

Field: | A field is a ring in which every nonzero element has a multiplicative inverse. The real numbers and the complex numbers are both fields. |

Ring: | In mathematics, a ring is an Abelian group together with a rule for multiplying its elements. |

i: |
i is the symbol used to denote the principal square root of -1, also called the imaginary unit. |