## Table comparing quaternions, complex quaternions and
octonions

Subject: Re: Quaternions

From: sweetser@alum.mit.edu
(Doug B Sweetser)

Date: 1997/05/02

Message-Id:
<E9K2D7.8FE@world.std.com>

Newsgroups:
sci.physics.electromag,sci.physics.particle,sci.physics.relativity

A very short comparison shopping list:

A very short comparison shopping list
the algebra of |
complex numbers |
quaternions |
complex quaternions |
octonions |

defined over the field of |
reals |
reals |
complex numbers |
reals |

commutes with |
all |
scalars |
complex numbers |
scalars |

invertible |
always |
always |
sometimes |
always |

associative |
yes |
yes |
yes |
not |

arcwise-connected topological number field |
yes |
yes |
no |
yes |

This table shows why complex numbers, quaternions
and octonions are often

discussed together. Algebras are about
generalizing addition. Division

is not part of the basic definition
of an algebra.

Doug
Sweetser

http://world.std.com/~sweetser

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