quaternion

noncommutative extension of the real numbers
rdfs:label
"quaternion"@en
skos:altLabel
"Hamilton number"@en
schema:description
"noncommutative extension of the real numbers"@en
schema:dateModified "2026-11-01T16:44:36+00:00"^^xsd:dateTime
schema:version 2563474090
wikibase:identifiers 33
wikibase:sitelinks 75
wikibase:statements 71
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p:P691 wd:statement/Q173853-EB5C35DB-0D0A-4549-8920-2A2EEBE86BEB
p:P7235 wd:statement/Q173853-5dc4664e-4618-57a5-0aa0-dcf6d02e5c60
wd:statement/Q173853-7915d577-4a36-fcad-b484-4de508f94bb8
wd:statement/Q173853-7ea5d169-463d-79a9-9f48-a9e830c0ba44
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p:P7554 wd:statement/Q173853-23ad7877-45eb-9600-c2b8-02d619ccb480
p:P8189 wd:statement/Q173853-C71321E9-C982-4B82-8C2A-B4EE496DE452
p:P8313 wd:statement/Q173853-343E1FC0-5AA5-48E0-A578-15A2AC3BA2B5
p:P8885 wd:statement/Q173853-8ca23792-421c-dcee-043a-a3858fe3463d
p:P910 wd:statement/Q173853-2232F87E-3905-44DE-B9D9-26C69BD96892
p:P950 wd:statement/Q173853-d16c50ee-43bd-dc17-0f97-615ffdd151a9
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wd:statement/Q173853-FE34F853-713F-41E4-8909-EBC3287E96B9
p:direct-normalized/P2163 <http://id.worldcat.org/fast/1085499>
p:direct-normalized/P227 <https://d-nb.info/gnd/4176653-2>
p:direct-normalized/P244 <http://id.loc.gov/authorities/names/sh85109754>
p:direct-normalized/P268 <http://data.bnf.fr/ark:/12148/cb11981947w#about>
p:direct-normalized/P3285 <http://msc2010.org/resources/MSC/2010/11R52>
p:direct-normalized/P349 <http://id.ndl.go.jp/auth/ndlna/00570899>
p:direct-normalized/P6366 <https://makg.org/entity/200127275>
p:direct-normalized/P950 <https://datos.bne.es/resource/XX4728834>
wdt:P10283 "C200127275"
wdt:P11514 "kvaterniony-3891da"
wdt:P13204 "j2h6986r"
wdt:P1343 Meyers Konversations-Lexikon, 4th edition (1885–1890)
Granat Encyclopedic Dictionary
Encyclopædia Britannica 11th edition
wdt:P13591 "concept/7f1924b7-aba6-4ee3-8e5a-fc51d50a3951"
wdt:P1368 "000137096"
wdt:P1417 "topic/quaternion"
wdt:P1482 <https://blender.stackexchange.com/tags/quaternion>
<https://computergraphics.stackexchange.com/tags/quaternions>
<https://gamedev.stackexchange.com/tags/quaternion>
<https://hsm.stackexchange.com/tags/quaternions>
<https://math.stackexchange.com/tags/quaternions>
<https://mathematica.stackexchange.com/tags/quaternions>
<https://mathoverflow.net/tags/quaternions>
<https://space.stackexchange.com/tags/quaternion>
<https://stackoverflow.com/tags/quaternions>
wdt:P155 complex number
wdt:P156 octonion
wdt:P1801 <http://commons.wikimedia.org/wiki/Special:FilePath/Inscription%20on%20Broom%20Bridge%20%28Dublin%29%20regarding%20the%20discovery%20of%20Quaternions%20multiplication%20by%20Sir%20William%20Rowan%20Hamilton.jpg>
wdt:P189 Broom Bridge
wdt:P2163 "1085499"
wdt:P227 "4176653-2"
wdt:P244 "sh85109754"
wdt:P2534 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>a</mi><mo stretchy="false">+</mo><mi>b</mi><mi>i</mi><mo stretchy="false">+</mo><mi>c</mi><mi>j</mi><mo stretchy="false">+</mo><mi>d</mi><mi>k</mi><mo>,</mo><mspace width="1em"></mspace><msup><mi>i</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msup><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msup><mi>k</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><mi>i</mi><mi>j</mi><mi>k</mi><mo stretchy="false">=</mo><mo stretchy="false">&#x2212;</mo><mn>1</mn></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>a</mi><mo stretchy="false">+</mo><mi>b</mi><mi>i</mi><mo stretchy="false">+</mo><mi>c</mi><mi>j</mi><mo stretchy="false">+</mo><mi>d</mi><mi>k</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math xmlns="http://www.w3.org/1998/Math/MathML" class="mwe-math-element mwe-math-element-inline"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><msup><mi>i</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msup><mi>j</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><msup><mi>k</mi><mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup><mo stretchy="false">=</mo><mi>i</mi><mi>j</mi><mi>k</mi><mo stretchy="false">=</mo><mo stretchy="false">−</mo><mn>1</mn></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P268 "11981947w"
wdt:P279 hypercomplex number
wdt:P2812 "Quaternion"
wdt:P3285 "11R52"
wdt:P3365 "quaternione"
wdt:P3417 "Quaternions-mathematics"
wdt:P349 "00570899"
wdt:P361 algebra of real quaternions
wdt:P373 "Quaternions"
wdt:P3827 "quaternions"
wdt:P3847 "quaternions"
wdt:P4215 "quaternion"
wdt:P4223 "quaternioni"
wdt:P4342 "kvaternioner"
wdt:P527 real number
wdt:P5555 <http://commons.wikimedia.org/wiki/Special:FilePath/Cayley%20Q8%20multiplication%20graph.svg>
<http://commons.wikimedia.org/wiki/Special:FilePath/Quaternion-multiplication-table.png>
<http://commons.wikimedia.org/wiki/Special:FilePath/Quaternions%20SO%283%29%20cube.svg>
wdt:P571 "1843-01-01T00:00:00+00:00"^^xsd:dateTime
wdt:P575 "1843-10-16T00:00:00+00:00"^^xsd:dateTime
wdt:P6058 "divers/quaternion/84765"
wdt:P61 William Rowan Hamilton
wdt:P6104 WikiProject Mathematics
wdt:P6366 "200127275"
wdt:P646 "/m/0dkqr"
wdt:P6781 "Definition:Quaternion"
wdt:P6900 "四元数"
wdt:P691 "ph844096"
wdt:P7235 "<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>a</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><mrow data-mjx-texclass="ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>i</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML
"<math class="mwe-math-element mwe-math-element-inline" xmlns="http://www.w3.org/1998/Math/MathML"><msup> <mrow data-mjx-texclass="ORD"><mn>2</mn></mrow></msup></math>"^^http://www.w3.org/1998/Math/MathML
wdt:P7305 "3929640"
wdt:P7554 "Quaternion"
wdt:P8189 "987007553303805171"
wdt:P8313 "kvaternioner"
wdt:P8885 "사원수"
wdt:P910 Category:Quaternions
wdt:P950 "XX4728834"
wdt:P973 <http://www.treccani.it/enciclopedia/quaternione_%28Dizionario-delle-Scienze-Fisiche%29/>
<https://getpocket.com/explore/item/the-strange-numbers-that-birthed-modern-algebra?utm_source=pocket-newtab-global-en-GB>
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