octonion

English

Etymology

Blend of Latin octō (“eight”) +‎ quaternion.

Noun

octonion (plural octonions)

1. (mathematics) An 8-dimensional nonassociative extension of a quaternion with a real part and 7 imaginary parts (each a real multiple of a distinct square root of −1).
   • 2022, Zlatka Valkova-Jarvis, Vladimir Poulkov, Viktor Stoynov, Dimitriya Mihaylova, Georgi Iliev, “A Method for the Design of Bicomplex Orthogonal DSP Algorithms for Applications in Intelligent Radio Access Networks”, in Symmetry, volume 14, number 3, MDPI AG, →DOI, →ISSN:

     According to the logic of doubling the dimensions on which Cayley–Dickson algebra is built, after quaternions the so-called 8D octonions ($\mathbb {O}$—Octonions) can be obtained, followed by 16D sedenions, 32D pathions, 64D chingons, 128D routons, and 256D voudons.

   • 2023, Melanie Swan, Renato P. dos Santos, “Quantum Intelligence: Responsible Human-AI Entities”, in AAAI 2023 Spring Symposia, Socially Responsible AI for Wellbeing, March 27–29, 2023, USA, CEUR Workshop Proceedings, →DOI:

     There is no theoretical limit to multispace dimensional numbering as there are definitions for octonion (8D), sedenion (16D), pathion (32D), chingon (64D), routon (128D), and voudon (256D) numbered space.

Hypernyms

• hypercomplex number

Translations

nonassociative extension of a quaternion

• French: octonion (fr) m
• German: Oktave (de) f, Oktonion f
• Icelandic: áttundatala f
• Italian: ottonione m, ottetto (it) m
• Russian: октонио́н m (oktonión)
• Spanish: octonión m

See also

• imaginary unit
• quaternion
• sedenion

Anagrams

• otoconin