Category:Definitions/Octonions

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This category contains definitions related to Octonions.
Related results can be found in Category:Octonions.


The set of octonions, usually denoted $\Bbb O$, can be defined by using the Cayley-Dickson construction from the quaternions $\H$ as follows:

From Quaternions form Algebra, $\H$ forms a nicely normed $*$-algebra.

Let $a, b \in \H$.

Then $\tuple {a, b} \in \Bbb O$, where:

$\tuple {a, b} \tuple {c, d} = \tuple {a c - d \overline b, \overline a d + c b}$
$\overline {\tuple {a, b} } = \tuple {\overline a, -b}$

where:

$\overline a$ is the conjugate of $a$

and

$\overline {\tuple {a, b} }$ is the conjugation operation on $\Bbb O$.

Pages in category "Definitions/Octonions"

The following 5 pages are in this category, out of 5 total.