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