| http://schema.org/description
|
estensione non associativa dei quaternioni
, algèbre non commutative et non associative de nombres avec huit composantes réelles
, non-commutative, non-associative algebra of numbers with eight real components
, nekomuta, neasocieca sistemo de nombroj kun ok realnombraj komponantoj
, 四元数的一个非结合推广
, álgebra não associativa não comutativa de números com oito componentes reais
, struktura algebraiczna rozszerzająca kwaterniony
, מונח מתמטי
, система гиперкомплексных чисел
, extensión no asociativa de los números reales
|
| http://schema.org/name
|
Oktave
, أوكتونيون
, Octonió
, oktonion
, octonion
, octonión
, Oktonioi
, اکتنیون
, אוקטוניונים
, ottetto
, 八元数
, 팔원수
, Numerus octonus
, oktawy Cayleya
, octoniões
, Алгебра Кэли
, Oktonion
, Октоніони
, Octonion
, octônios
, 八元數
, okopnombro
, ออกโทเนียน
, Οκτόνιο
, актаніён
, Кэли алгебри
, Októniók
|
| http://www.w3.org/2004/02/skos/core#altLabel
|
oktoniony
, liczby Cayleya
, octonion
, oktoniono
, nombro de Cayley
, Cayley number
, octave
, octonions
, Cayley numbers
, octaves
, ottonione
, ottonioni
, ottetti
, Numeri di Cayley
, Numero di Cayley
, ottetti di Cayley
, 8元数
, 八元數
, 8元數
, Cayley-Zahlen
, Cayley-Zahl
, Oktonionen
, Cayleyzahlen
, Cayleyzahl
, nombres de Cayley
, octaves de Cayley
, актава Кэйлея
|
| http://www.w3.org/2004/02/skos/core#prefLabel
|
Oktave
, أوكتونيون
, Octonió
, oktonion
, octonion
, octonión
, Oktonioi
, اکتنیون
, אוקטוניונים
, ottetto
, 八元数
, 팔원수
, Numerus octonus
, oktawy Cayleya
, octoniões
, Алгебра Кэли
, Oktonion
, Октоніони
, Octonion
, octônios
, 八元數
, okopnombro
, ออกโทเนียน
, Οκτόνιο
, актаніён
, Кэли алгебри
, Októniók
|
| http://www.wikidata.org/prop/P10376
|
http://www.wikidata.org/entity/statement/Q743418-c3502535-4d3b-ae70-cc2a-df854db92c7e +
|
| http://www.wikidata.org/prop/P1482
|
http://www.wikidata.org/entity/statement/Q743418-3d2793d8-4f1f-6fdc-cbf4-a843770fac16 +
, http://www.wikidata.org/entity/statement/Q743418-265f0edb-486f-b2b6-47f5-70d808d54076 +
|
| http://www.wikidata.org/prop/P155
|
http://www.wikidata.org/entity/statement/Q743418-6e65700e-4031-5869-d600-09711a6b88a0 +
|
| http://www.wikidata.org/prop/P156
|
http://www.wikidata.org/entity/statement/Q743418-c7a31b70-4d65-20d6-6e19-a176c455e7be +
|
| http://www.wikidata.org/prop/P18
|
http://www.wikidata.org/entity/statement/Q743418-6aed76fa-417b-14a4-6d4b-e9d8825f111f +
|
| http://www.wikidata.org/prop/P2163
|
http://www.wikidata.org/entity/statement/Q743418-8fd284d3-4afe-2582-b92c-e4639c747270 +
|
| http://www.wikidata.org/prop/P227
|
http://www.wikidata.org/entity/statement/Q743418-72f8bc03-4e6e-3de7-69f8-c5efe6d9c4c3 +
|
| http://www.wikidata.org/prop/P244
|
http://www.wikidata.org/entity/statement/Q743418-AE654345-E1EA-42DC-878E-A904C0DA1E66 +
|
| http://www.wikidata.org/prop/P2534
|
http://www.wikidata.org/entity/statement/Q743418-e98092be-4e38-50b9-03b0-9d7356bf2149 +
|
| http://www.wikidata.org/prop/P268
|
http://www.wikidata.org/entity/statement/Q743418-613d713f-469e-fac0-c0d5-47a6c27bddf0 +
|
| http://www.wikidata.org/prop/P269
|
http://www.wikidata.org/entity/statement/Q743418-11c0cc15-47a6-d3bb-3d45-b600125a4d3b +
|
| http://www.wikidata.org/prop/P279
|
http://www.wikidata.org/entity/statement/Q743418-5a52e529-49a6-234c-5293-26e2fa677d62 +
, http://www.wikidata.org/entity/statement/Q743418-a6e0c32d-458a-2cc3-f52d-c05bc377f1c7 +
, http://www.wikidata.org/entity/statement/Q743418-ae7a6177-42f0-e0b7-dcf2-47b162a6f045 +
, http://www.wikidata.org/entity/statement/Q743418-8a88b442-46d8-dca7-e482-d44787247d55 +
, http://www.wikidata.org/entity/statement/Q743418-f9560e22-4223-54e6-aed4-910b8e8d40cf +
|
| http://www.wikidata.org/prop/P2812
|
http://www.wikidata.org/entity/statement/Q743418-E3F9C42F-6B18-42C6-8B90-EB8884AAE28B +
, http://www.wikidata.org/entity/statement/Q743418-A2978209-AA93-4ED1-AF54-47B99C31FBFE +
|
| http://www.wikidata.org/prop/P31
|
http://www.wikidata.org/entity/statement/Q743418-70ef22c0-48d9-ca4b-952c-588f507c95a5 +
, http://www.wikidata.org/entity/statement/Q743418-565fa215-4265-062c-c02b-6f874dbb2bf9 +
|
| http://www.wikidata.org/prop/P361
|
http://www.wikidata.org/entity/statement/Q743418-4b7746c3-443b-2a1b-6fbd-ddef92ac3ea8 +
|
| http://www.wikidata.org/prop/P373
|
http://www.wikidata.org/entity/statement/Q743418-655630B4-A8A7-4071-8A0F-39B2B371C648 +
|
| http://www.wikidata.org/prop/P4215
|
http://www.wikidata.org/entity/statement/Q743418-E335E0D6-8FFB-4458-B7BC-73873DBFD648 +
|
| http://www.wikidata.org/prop/P527
|
http://www.wikidata.org/entity/statement/Q743418-0bc2cd71-40ef-901d-32cb-3841948948a2 +
|
| http://www.wikidata.org/prop/P575
|
http://www.wikidata.org/entity/statement/Q743418-39ca2545-48cc-b7af-c474-7680bd45b7c5 +
|
| http://www.wikidata.org/prop/P61
|
http://www.wikidata.org/entity/statement/Q743418-74d79f63-4bfe-909f-482a-2841f547bf32 +
|
| http://www.wikidata.org/prop/P6104
|
http://www.wikidata.org/entity/statement/Q743418-1D166FCF-D1DD-4BB2-AC6B-46D4FBE38079 +
|
| http://www.wikidata.org/prop/P6366
|
http://www.wikidata.org/entity/statement/Q743418-D1C06324-B320-47BB-A4AC-9C27FD31A0E6 +
|
| http://www.wikidata.org/prop/P646
|
http://www.wikidata.org/entity/statement/Q743418-D14DD54E-08E1-4C1B-9DA0-8CD5D00BDAFE +
|
| http://www.wikidata.org/prop/P6781
|
http://www.wikidata.org/entity/statement/Q743418-c15b5d25-4822-b515-d1f7-408c9ae96dad +
|
| http://www.wikidata.org/prop/P7235
|
http://www.wikidata.org/entity/statement/Q743418-e4791195-4aa8-5ace-4e66-1715c5a8b38c +
, http://www.wikidata.org/entity/statement/Q743418-2fdc688d-442a-bffd-568b-94b77ef2e0b6 +
|
| http://www.wikidata.org/prop/P8189
|
http://www.wikidata.org/entity/statement/Q743418-CDD55727-871E-48D6-92E8-E82673D8ADF4 +
|
| http://www.wikidata.org/prop/P910
|
http://www.wikidata.org/entity/statement/Q743418-2F62D871-29EE-4CAC-98EA-6E10A8CC7735 +
|
| http://www.wikidata.org/prop/direct-normalized/P2163
|
http://id.worldcat.org/fast/849971 +
|
| http://www.wikidata.org/prop/direct-normalized/P227
|
https://d-nb.info/gnd/4745179-8 +
|
| http://www.wikidata.org/prop/direct-normalized/P244
|
http://id.loc.gov/authorities/names/sh2002008702 +
|
| http://www.wikidata.org/prop/direct-normalized/P268
|
http://data.bnf.fr/ark:/12148/cb15608111r#about +
|
| http://www.wikidata.org/prop/direct-normalized/P269
|
http://www.idref.fr/122706331/id +
|
| http://www.wikidata.org/prop/direct-normalized/P6366
|
https://makg.org/entity/2779181008 +
|
| http://www.wikidata.org/prop/direct/P10376
|
mathematics/octonions
|
| http://www.wikidata.org/prop/direct/P1482
|
https://mathoverflow.net/tags/octonions +
, https://math.stackexchange.com/tags/octonions +
|
| http://www.wikidata.org/prop/direct/P155
|
http://www.wikidata.org/entity/Q173853 +
|
| http://www.wikidata.org/prop/direct/P156
|
http://www.wikidata.org/entity/Q79188 +
|
| http://www.wikidata.org/prop/direct/P18
|
http://commons.wikimedia.org/wiki/Special:FilePath/Octonionstar123.png +
|
| http://www.wikidata.org/prop/direct/P2163
|
849971
|
| http://www.wikidata.org/prop/direct/P227
|
4745179-8
|
| http://www.wikidata.org/prop/direct/P244
|
sh2002008702
|
| http://www.wikidata.org/prop/direct/P2534
|
<math xmlns="http://www.w3.org/1998/Mat … <math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle {\begin{aligned}\mathbb {O} &=\{a_{0}+a_{1}e_{1}+\dotsb +a_{7}e_{7}\;\mid \;a_{0},\dotsc ,a_{7}\in \mathbb {R} \}\\e_{i}e_{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}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true">
<mtr>
<mtd>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">O</mi>
</mrow>
</mtd>
<mtd>
<mi></mi>
<mo>=</mo>
<mo fence="false" stretchy="false">{</mo>
<msub>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<msub>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<mo>⋯<!-- ⋯ --></mo>
<mo>+</mo>
<msub>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>7</mn>
</mrow>
</msub>
<msub>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>7</mn>
</mrow>
</msub>
<mspace width="thickmathspace" />
<mo>∣<!-- ∣ --></mo>
<mspace width="thickmathspace" />
<msub>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>0</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>…<!-- … --></mo>
<mo>,</mo>
<msub>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>7</mn>
</mrow>
</msub>
<mo>∈<!-- ∈ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="double-struck">R</mi>
</mrow>
<mo fence="false" stretchy="false">}</mo>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
<msub>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>j</mi>
</mrow>
</msub>
</mtd>
<mtd>
<mi></mi>
<mo>=</mo>
<mo>−<!-- − --></mo>
<msub>
<mi>δ<!-- δ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>c</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msub>
<msub>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>k</mi>
</mrow>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>c</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mi>j</mi>
<mi>k</mi>
</mrow>
</msub>
</mtd>
<mtd>
<mi></mi>
<mo>=</mo>
<mrow class="MJX-TeXAtom-ORD">
<mrow>
<mo>{</mo>
<mtable columnalign="left left" rowspacing=".2em" columnspacing="1em" displaystyle="false">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mrow class="MJX-TeXAtom-ORD">
<mtext>even perm. of </mtext>
</mrow>
<mn>123</mn>
<mo>,</mo>
<mn>145</mn>
<mo>,</mo>
<mn>176</mn>
<mo>,</mo>
<mn>246</mn>
<mo>,</mo>
<mn>257</mn>
<mo>,</mo>
<mn>347</mn>
<mo>,</mo>
<mn>365</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mtd>
<mtd>
<mrow class="MJX-TeXAtom-ORD">
<mtext>odd perm. of </mtext>
</mrow>
<mn>123</mn>
<mo>,</mo>
<mn>145</mn>
<mo>,</mo>
<mn>176</mn>
<mo>,</mo>
<mn>246</mn>
<mo>,</mo>
<mn>257</mn>
<mo>,</mo>
<mn>347</mn>
<mo>,</mo>
<mn>365</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mrow class="MJX-TeXAtom-ORD">
<mtext>otherwise</mtext>
</mrow>
</mtd>
</mtr>
</mtable>
<mo fence="true" stretchy="true" symmetric="true"></mo>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\mathbb {O} &=\{a_{0}+a_{1}e_{1}+\dotsb +a_{7}e_{7}\;\mid \;a_{0},\dotsc ,a_{7}\in \mathbb {R} \}\\e_{i}e_{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}}}</annotation>
</semantics>
</math>ion>
</semantics>
</math>
|
| http://www.wikidata.org/prop/direct/P268
|
15608111r
|
| http://www.wikidata.org/prop/direct/P269
|
122706331
|
| http://www.wikidata.org/prop/direct/P279
|
http://www.wikidata.org/entity/Q837414 +
|
| http://www.wikidata.org/prop/direct/P2812
|
Octonion
, CayleyNumber
|
| http://www.wikidata.org/prop/direct/P31
|
http://www.wikidata.org/entity/Q2165111 +
, http://www.wikidata.org/entity/Q2835924 +
|
| http://www.wikidata.org/prop/direct/P361
|
http://www.wikidata.org/entity/Q2835924 +
|
| http://www.wikidata.org/prop/direct/P373
|
Octonions
|
| http://www.wikidata.org/prop/direct/P4215
|
octonion
|
| http://www.wikidata.org/prop/direct/P527
|
http://www.wikidata.org/entity/Q173853 +
|
| http://www.wikidata.org/prop/direct/P575
|
"1843-01-01T00:00:00Z"^^xsd:dateTime
|
| http://www.wikidata.org/prop/direct/P61
|
http://www.wikidata.org/entity/Q940427 +
|
| http://www.wikidata.org/prop/direct/P6104
|
http://www.wikidata.org/entity/Q8487137 +
|
| http://www.wikidata.org/prop/direct/P6366
|
2779181008
|
| http://www.wikidata.org/prop/direct/P646
|
/m/0dkps
|
| http://www.wikidata.org/prop/direct/P6781
|
Definition:Octonion
|
| http://www.wikidata.org/prop/direct/P7235
|
<math xmlns="http://www.w3.org/1998/Mat … <math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle \delta _{ij}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>δ<!-- δ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \delta _{ij}}</annotation>
</semantics>
</math>ion>
</semantics>
</math>
, <math xmlns="http://www.w3.org/1998/Mat … <math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="{\displaystyle e_{i}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>i</mi>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle e_{i}}</annotation>
</semantics>
</math>ion>
</semantics>
</math>
|
| http://www.wikidata.org/prop/direct/P8189
|
987007558916605171
|
| http://www.wikidata.org/prop/direct/P910
|
http://www.wikidata.org/entity/Q10179671 +
|
| rdf:type |
http://wikiba.se/ontology#Item +
|
| rdfs:label |
Oktave
, أوكتونيون
, Octonió
, oktonion
, octonion
, octonión
, Oktonioi
, اکتنیون
, אוקטוניונים
, ottetto
, 八元数
, 팔원수
, Numerus octonus
, oktawy Cayleya
, octoniões
, Алгебра Кэли
, Oktonion
, Октоніони
, Octonion
, octônios
, 八元數
, okopnombro
, ออกโทเนียน
, Οκτόνιο
, актаніён
, Кэли алгебри
, Októniók
|
