Sedenione

I sedenioni (anche chiamati esadecanioni) formano un'algebra a 16 dimensioni sul campo dei numeri reali; questa può considerarsi ottenuta applicando la costruzione di Cayley-Dickson sull'algebra degli ottetti.

Come per gli ottetti, la moltiplicazione dei sedenioni non è né commutativaassociativa.

A differenza degli ottetti, i sedenioni non hanno la proprietà dell'algebra alternativa, ma mantengono quella della potenza associativa. I sedenioni hanno l'elemento unità della moltiplicazione e molti sedenioni sono invertibili; essi, però, non costituiscono un'algebra di divisione, dato che alcuni di essi sono divisori dello zero.

I sedenioni si possono ottenere come combinazioni lineari dei seguenti sedenioni invertibili: 1, e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11, e12, e13, e14, e15. In altre parole i precedenti elementi costituiscono una base dello spazio vettoriale dei sedenioni. Come si vede tutti questi elementi sono invertibili, cioè unità.

La matrice moltiplicativa delle unità dei sedenioni è presentata qui sotto.

× 1
e1
e2
e3
e4
e5
e6
e7
e8
e9
e10
e11
e12
e13
e14
e15
1
1
e1
e2
e3
e4
e5
e6
e7
e8
e9
e10
e11
e12
e13
e14
e15
e1
e1
-1
e3
-e2
e5
-e4
-e7
e6
e9
-e8
-e11
e10
-e13
e12
e15
-e14
e2
e2
-e3
-1
e1
e6
e7
-e4
-e5
e10
e11
-e8
-e9
-e14
-e15
e12
e13
e3
e3
e2
-e1
-1
e7
-e6
e5
-e4
e11
-e10
e9
-e8
-e15
e14
-e13
e12
e4
e4
-e5
-e6
-e7
-1
e1
e2
e3
e12
e13
e14
e15
-e8
-e9
-e10
-e11
e5
e5
e4
-e7
e6
-e1
-1
-e3
e2
e13
-e12
e15
-e14
e9
-e8
e11
-e10
e6
e6
e7
e4
-e5
-e2
e3
-1
-e1
e14
-e15
-e12
e13
e10
-e11
-e8
e9
e7
e7
-e6
e5
e4
-e3
-e2
e1
-1
e15
e14
-e13
-e12
e11
e10
-e9
-e8
e8
e8
-e9
-e10
-e11
-e12
-e13
-e14
-e15
-1
e1
e2
e3
e4
e5
e6
e7
e9
e9
e8
-e11
e10
-e13
e12
e15
-e14
-e1
-1
-e3
e2
-e5
e4
e7
-e6
e10
e10
e11
e8
-e9
-e14
-e15
e12
e13
-e2
e3
-1
-e1
-e6
-e7
e4
e5
e11
e11
-e10
e9
e8
-e15
e14
-e13
e12
-e3
-e2
e1
-1
-e7
e6
-e5
e4
e12
e12
e13
e14
e15
e8
-e9
-e10
-e11
-e4
e5
e6
e7
-1
-e1
-e2
-e3
e13
e13
-e12
e15
-e14
e9
e8
e11
-e10
-e5
-e4
e7
-e6
e1
-1
e3
-e2
e14
e14
-e15
-e12
e13
e10
-e11
e8
e9
-e6
-e7
-e4
e5
e2
-e3
-1
e1
e15
e15
e14
-e13
-e12
e11
e10
-e9
e8
-e7
e6
-e5
-e4
e3
e2
-e1
-1

Altre letture

  • (EN) Carmody, Kevin: Circular and Hyperbolic Quaternions, Octonions and Sedenions, Applied Mathematics and Computation 28:47-72 (1988)
  • (EN) Carmody, Kevin: Circular and Hyperbolic Quaternions, Octonions and Sedenions - Further results, Applied Mathematics and Computation, 84:27-47 (1997)
  • (EN) Imaeda, K., Imaeda, M.: Sedenions: algebra and analysis, Applied Mathematics and Computation, 115:77-88 (2000)

Altri progetti

  Portale Matematica: accedi alle voci di Wikipedia che trattano di matematica

Read other articles:

Historic site in New South Wales, AustraliaGrossmann HouseGrossmann House, 2017Location71 Church Street, Maitland, City of Maitland, New South Wales, AustraliaCoordinates32°44′07″S 151°33′10″E / 32.7353°S 151.5528°E / -32.7353; 151.5528Built1860–1862OwnerNational Trust of Australia (NSW) New South Wales Heritage RegisterOfficial nameGrossman House; Brough and Grossmann House Group; Maitland Girl’s High School; Grossmann HouseTypestate heritage (buil...

 

Manuel Edmundo Montesinos Muñoz Senador de la República del Perúpor Cusco 28 de julio de 1911-25 de octubre de 1916Presidente Augusto B. LeguíaGuillermo BillinghurstOscar R. BenavidesJosé Pardo y Barreda Información personalNacimiento 1860Arequipa, Perú PerúFallecimiento 1 de junio de 1919 (59 años)Cusco, Perú PerúNacionalidad PeruanaCiudadanía PeruanaFamiliaPadres José Benito MontesinosEnriqueta MuñozCónyuge María Josefina Velasco del CastilloAntonia Velasco del CastilloHijos...

 

هذه المقالة يتيمة إذ تصل إليها مقالات أخرى قليلة جدًا. فضلًا، ساعد بإضافة وصلة إليها في مقالات متعلقة بها. (يوليو 2019) ماكس كولي معلومات شخصية الميلاد 21 فبراير 1931  ملبورن  تاريخ الوفاة 6 يناير 2018 (86 سنة)   مواطنة أستراليا  الحياة العملية المهنة عازف مترددة  [لغات أ

Dewan Perwakilan RakyatPapua BaratPeriode 2019-2024JenisJenisUnikameral Jangka waktu5 tahunSejarahDidirikan2003Sesi baru dimulai2 Oktober 2019PimpinanKetuaOrgenes Wonggor (Golkar) sejak 5 Desember 2019 Wakil Ketua IRenly Mansawan (NasDem) sejak 5 Desember 2019 Wakil Ketua IISaleh Siknun (PDI-P) sejak 5 Desember 2019 Wakil Ketua IIIYongki Roberto Fonataba (Demokrat) sejak 5 Desember 2019 KomposisiAnggota56Partai & kursiPemerintah (19)   PDI-P (7)   NasDe...

 

?†ChasmaporthetesЧас існування: пліоцен — плейстоцен, 4,9 — 0,78 млн років тому Череп C. lunensis Біологічна класифікація Домен: Еукаріоти (Eukaryota) Царство: Тварини (Animalia) Тип: Хордові (Chordata) Клас: Ссавці (Mammalia) Ряд: Хижі (Carnivora) Родина: Гієнові (Hyaenidae) Рід: †ChasmaporthetesHay, 1921 Види Див.текс

 

Усипальниця мовчання Ідеа́льний пала́ц Фердіна́нда Шева́ля (фр. Le Palais Idéal) – палац, побудований листоношею Фердінандом Шевалем. Знаходиться у департаменті Дром, містечку Отерів, недалеко від Ліона. Зміст 1 Історія створення 2 Архітектурні особливості 3 Визнання 4 Джерела 5

Arsitek di depan papan gambarnya, 1893. Arsitek atau seniman bina adalah seorang ahli di bidang ilmu arsitektur, ahli rancang bangun atau ahli lingkungan binaan. Istilah arsitek sering kali diartikan secara sempit sebagai seorang perancang bangunan, adalah orang yang terlibat dalam perencanaan, merancang, dan mengawasi konstruksi bangunan, yang perannya untuk memandu keputusan yang memengaruhi aspek bangunan tersebut dalam sisi astetika, budaya, atau masalah sosial. Definisi tersebut kurangla...

 

United States federal prison in Florida This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources.Find sources: Federal Correctional Complex, Coleman – news · newspapers · books...

 

Croatian basketball player and coach Krešimir ĆosićĆosić with Yugoslavia in 1970Personal informationBorn(1948-11-26)26 November 1948Zagreb, PR Croatia, FPR YugoslaviaDied25 May 1995(1995-05-25) (aged 46)Baltimore, Maryland, U.S.NationalityYugoslavianCroatianListed height6 ft 11 in (2.11 m)Listed weight212 lb (96 kg)Career informationCollegeBYU (1970–1973)NBA draft1973: 5th round, 84th overall pickSelected by the Los Angeles LakersPlaying career1964–1983P...

American human rights activist The neutrality of this article is disputed. Relevant discussion may be found on the talk page. Please do not remove this message until conditions to do so are met. (January 2021) (Learn how and when to remove this template message) Ajamu BarakaBornAjamu Sibeko Baraka (1953-10-25) October 25, 1953 (age 70)Chicago, Illinois, U.S.EducationCity College of New YorkUniversity of South Florida (BA)Clark Atlanta University (MA, PhD)Political partyGreenMilitary care...

 

Bangladeshi politician Habiba Rahman KhanMember of Bangladesh ParliamentIncumbentAssumed office 2019 Personal detailsPolitical partyBangladesh Awami League Habiba Rahman Khan is a Bangladesh Awami League politician and a Member of Bangladesh Parliament from a reserved seat.[1] Career Khan was elected to parliament from reserved seat as a Bangladesh Awami League candidate in 2019.[2] References ^ AL finalises 41 for women JS seats. unb.com.bd. Retrieved 3 April 2020. ^ Arom...

 

Poppenricht Lambang kebesaranLetak Poppenricht di Amberg-Sulzbach NegaraJermanNegara bagianBayernWilayahOberpfalzKreisAmberg-SulzbachSubdivisions9 OrtsteilePemerintahan • MayorFranz Birkl (CSU)Luas • Total11,58 km2 (447 sq mi)Ketinggian406 m (1,332 ft)Populasi (2013-12-31)[1] • Total3.359 • Kepadatan2,9/km2 (7,5/sq mi)Zona waktuWET/WMPET (UTC+1/+2)Kode pos92284Kode area telepon09621Pelat kendaraanASSitu...

This is an alphabetical list of countries by past and projected gross domestic product (nominal) as ranked by the IMF. Figures are based on official exchange rates, not on the purchasing power parity (PPP) methodology. Values are given in millions of United States dollars (USD) and have not been adjusted for inflation. These figures have been taken from the International Monetary Fund's World Economic Outlook (WEO) Database (October 2023 edition) and/or other sources.[1] For older GDP...

 

Indian Politician (born 1956) Raosaheb Danve PatilMinister of State for RailwaysIncumbentAssumed office 7 July 2021Serving with Darshana JardoshPresidentRam Nath KovindPrime MinisterNarendra ModiMinisterAshwini VaishnawPreceded bySuresh AngadiMinister of State for CoalIncumbentAssumed office 7 July 2021PresidentRam Nath KovindPrime MinisterNarendra ModiMinisterPralhad JoshiMinister of State for MinesIncumbentAssumed office 7 July 2021PresidentRam Nath KovindPrime MinisterN...

 

This article includes a list of references, related reading, or external links, but its sources remain unclear because it lacks inline citations. Please help to improve this article by introducing more precise citations. (November 2018) (Learn how and when to remove this template message) Wenceslaus IDuke of LegnicaWenceslaus I of Legnica with his wife Anna of CieszynBornca. 1318Died2 June 1364Noble familySilesian PiastsSpouse(s)Anna of CieszynIssueRupert I of LegnicaWenceslaus IIBolesław IV...

Logo GFTI GFTI atau Grup Fisikawan Teoritik Indonesia (Indonesian Theoretical Physicist Group) adalah organisasi informal komunitas fisika teoritik di Indonesia. Fisika Teoritik sendiri didefinisikan sebagai semua sub-bidang fisika yang mengkaji aneka aspek ilmu fisika itu sendiri. Secara resmi GFTI berdiri tanggal 19 Mei 2004 saat Workshop on Theoretical Physics 2K4 di UI, Depok. Sebagai wadah informal fisikawan teoritik, berbeda dengan organisasi profesi ilmiah lainnya GFTI dikelola secara ...

 

American financial news and analysis blog Naked CapitalismHomepage dated November 1, 2014Type of siteFinancial news and analysisAvailable inEnglishOwnerAurora Advisors IncorporatedCreated byYves SmithURLwww.nakedcapitalism.comCommercialYesRegistrationNoneLaunchedDecember 2006; 17 years ago (2006-12)Current statusOnline Naked Capitalism is a liberal American group blog focused on the financial sector.[1][2] Susan Webber, the principal of Au...

 

Extinct baronetcy in the Baronetage of England This article relies largely or entirely on a single source. Relevant discussion may be found on the talk page. Please help improve this article by introducing citations to additional sources.Find sources: Bale baronets – news · newspapers · books · scholar · JSTOR (October 2022) The Bale Baronetcy, of Carleton Curlieu in the County of Leicester, was a title in the Baronetage of England. It was created on 3...

Fictional character on 30 Rock Fictional character Liz Lemon30 Rock characterLiz LemonFirst appearancePilot (2006)Last appearance30 Rock: A One-Time Special (2020)Created byTina FeyPortrayed byTina FeyJulia Louis-Dreyfus (during flashbacks in Live Show)Amy Poehler (during flashbacks in Live from Studio 6H)Michal Antonov (as a preteen in The Head and the Hair & Seinfeld Vision)Alice Richmond (as a preteen in Mazel Tov, Dummies!)Marcella Roy (as a preschooler in Rosemary's Baby & Kidnap...

 

American academic administrator and priest For other people named William Byron, see William Byron (disambiguation). The ReverendWilliam J. ByronSJPresident of the University of ScrantonIn office1975–1982Preceded byDexter L. Hanley, S.J.Succeeded byJoseph A. Panuska, S.J.President of the Catholic University of AmericaIn office1982–1992Preceded byEdmund D. Pellegrino, M.D.Succeeded byBrother Patrick Ellis, F.S.C.Interim President of Loyola University New OrleansIn office2003–2004Preceded...

 

Strategi Solo vs Squad di Free Fire: Cara Menang Mudah!