Octonions: Difference between revisions
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imported>Ragnar Schroder (→Definition & basic operations: fixing formula) |
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== Definition & basic operations == | == Definition & basic operations == | ||
The octonions, <math>\mathbb{O}</math>, are a eight-dimensional normed division algebra over the real numbers.<br/><br/> | The octonions, <math>\mathbb{O}</math>, are a eight-dimensional normed division algebra over the real numbers.<br/><br/> | ||
:<math>\mathbb{O}=\left\lbrace a_0 + \sum_{i= | :<math>\mathbb{O}=\left\lbrace a_0 + \sum_{i=1}^7a_i e_i|a_1, \dots, a_7 \in {\mathbb{R}}\right\rbrace</math><br/> | ||
== Properties == | == Properties == | ||
Revision as of 04:30, 19 December 2007
Octonions are a non-commutative and non-associative extension of the real numbers. They were were first discovered by John Graves, a friend of Sir William Rowan Hamilton who first described the related quaternions. Although Hamilton offered to publicize Graves discovery, it took Arthur Cayley to rediscover and publish in 1845, for this reason octonions are also known as Cayley Numbers.
Definition & basic operations
The octonions, , are a eight-dimensional normed division algebra over the real numbers.
Properties
Applications
See also
Related topics
References
External links
- Octonion at MathWorld