Table comparing quaternions, complex quaternions and octonions

Subject: Re: Quaternions
From: (Doug B Sweetser)
Date: 1997/05/02
Message-Id: <>
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
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

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