Category:Octonions
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This category contains results about Octonions.
Definitions specific to this category can be found in Definitions/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 "Octonions"
The following 2 pages are in this category, out of 2 total.