View source for Sedenion

{{also|Sedenion|sédénion|sedenión}}
==English==
{{wp}}

===Etymology===
{{blend|en|la:sēdecim<t:sixteen>|quaternion}}.

===Noun===
{{en-noun}}

# {{lb|en|mathematics}} A 16-dimensional nonalternative extension of an [[octonion]] with one real part and 15 imaginary parts, each a real multiple of a distinct, independent [[square root]] of −1.
#* {{quote-journal|en|last=Valkova-Jarvis|first=Zlatka|last2=Poulkov|first2=Vladimir|last3=Stoynov|first3=Viktor|last4=Mihaylova|first4=Dimitriya|last5=Iliev|first5=Georgi|title=A Method for the Design of Bicomplex Orthogonal DSP Algorithms for Applications in Intelligent Radio Access Networks|journal=Symmetry|publisher=MDPI AG|volume=14|issue=3|year=2022|issn=2073-8994|doi=10.3390/sym14030613|passage=According to the logic of doubling the dimensions on which Cayley–Dickson algebra is built, after quaternions the so-called 8D octonions (<math>\mathbb O</math>—Octonions) can be obtained, followed by 16D '''sedenions''', 32D pathions, 64D chingons, 128D routons, and 256D voudons.}}
#* {{quote-journal|en|year=2023|publisher=CEUR Workshop Proceedings|title=Quantum Intelligence: Responsible Human-AI Entities|work=AAAI 2023 Spring Symposia, Socially Responsible AI for Wellbeing, March 27–29, 2023, USA|author=Melanie Swan; Renato P. dos Santos|doi=10.48550/arXiv.math/0603281|passage=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.}}

====Synonyms====
* {{l|en|hexadecanion}}

====Hypernyms====
* {{l|en|hypercomplex number}}

====Derived terms====
* {{l|en|sedenionic}}

====Translations====
{{trans-top|nonassociative, nonalternative extension of an octonion}}
* Chinese:
*: Mandarin: {{t|cmn|十六元數|tr=shíliù-yuán shù}}
* Hungarian: {{t|hu|szedénió}}
* Icelandic: {{t|is|sextándatala|f}}
{{trans-bottom}}

===See also===
* {{l|en|quaternion}}
* {{l|en|octonion}}
* {{l|en|trigintaduonion}}

===Further reading===
* {{pedia|Cayley–Dickson construction}}

===Anagrams===
* {{anagrams|en|a=deeinnos|dienones|nesodine}}

{{C|en|Higher-dimensional geometry|Sixteen}}