octonion
non-commutative, non-associative algebra of numbers with eight real components
Facts
11 properties- Instance of
- alternative algebra, octonion algebra[7]
- Follows
- quaternion[8]
- Subclass of
- 8-tuple, 4-tuple, ordered pair, sedenion, hypercomplex number[10]
- Part of
- octonion algebra[11]
- Defining formula
- \begin{aligned}\mathbb O&=\{a_0+a_1e_1+\dotsb+a_7e_7\;\mid\; a_0,\dotsc,a_7\in\mathbb R\}\\e_ie_j&=-\delta_{ij}+c_{ijk}e_k\\c_{ijk}&=\begin{cases}1&\text{even perm. of }123,145, 176, 246, 257, 347, 365\\-1&\text{odd perm. of }123,145, 176, 246, 257, 347, 365\\0&\text{otherwise}\end{cases}\end{aligned}
- Discoverer or inventor
- John T. Graves[6]
- Has part(s)
- quaternion[12]
- In defining formula
- \delta_{ij}, e_i
- Maintained by WikiProject
- WikiProject Mathematics[14]
- Time of discovery or invention
- 1843[13]
🏷️ Also known as
en Cayley number
en Cayley numbers
en octave
en octaves
en octonions
en octonion
ar المثمان
ar اوكتونيون
ar أوكتونيون
ar عدد ثماني مركب
ar مثمان
cs oktonion
de Oktonionen
de Cayleyzahl
de Cayley-Zahl
de Cayleyzahlen
de Cayley-Zahlen
de Oktave
el οκτόνιο
es octonion
🔖 Identifiers · 17
- Library of Congress Authorities ID
- sh2002008702
- GND ID
- 4745179-8
- Image (Wikimedia Commons)
- Octonionstar123.png ↗
- Bibliothèque nationale de France ID
- 15608111r
- FAST ID
- 849971
- Freebase ID
- /m/0dkps
- IdRef ID
- 122706331
- J9U entity ID
- 987007558916605171
- MathWorld ID
- Octonion, CayleyNumber
- Microsoft Academic ID (discontinued)
- 2779181008
- NLab ID
- octonion
- Namuwiki ID
- 팔원수
Show all 17 identifiers +5
- ProofWiki ID
- Definition:Octonion
- ScienceDirect topic ID
- mathematics/octonions
- Stack Exchange tag
- mathoverflow.net, math.stackexchange.com
- Topic's main category
- Category:Octonions
- Yale LUX ID
- concept/55f53b31-2e07-4558-b872-9767f8de88cc
🔗 Connections
Subclass of 3
Belongs to 1
Created notable works 1
Discoverer or inventor 1
Followed by 1
Followed by (predecessor) 1
Follows 1
Has part(s) 1
Instance of 1
Maintained by WikiProject 1
Preceded by (successor) 1
Subtypes 1
← Characteristic of 1
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