orthogonal group
mathematical group consisting of transformations of a Euclidean space which preserve distance and a fixed point
| rdfs:label |
"orthogonal group"@en
|
|
skos:alt |
"O(n)"@en
"general orthogonal group"@en
|
| schema:description |
"mathematical group consisting of transformations of a Euclidean space which preserve distance and a fixed point"@en
|
|
schema:date |
"2026-09-06T20:24:44+00:00"^^xsd:dateTime |
| schema:version | 2541298337 |
| wikibase:identifiers | 9 |
| wikibase:sitelinks | 22 |
| wikibase:statements | 18 |
| p:P10283 | wd:statement/Q1783179-B7392EE3-7EE7-4958-982C-1A0052508CBC |
| p:P2534 | wd:statement/Q1783179-585c7123-4c52-d8d6-49bd-7722d9286742 |
| p:P2579 | wd:statement/Q1783179-755dd99a-4974-58ff-5ee9-9da2fe16e20c |
| wd:statement/Q1783179-C3D1C6AC-3273-4FB4-BE52-8EFF780724BD | |
| p:P279 | wd:statement/Q1783179-018dfac6-4392-0bc7-cdf2-bebf2f66e83e |
| wd:statement/Q1783179-3ec6d47c-486b-ff61-3b6a-7a089a26126b | |
| wd:statement/Q1783179-a2da6116-4a20-8e79-8e26-51e87a766e83 | |
| wd:statement/Q1783179-b6688a68-4516-bec5-a0d9-56c28a279c94 | |
| p:P2812 | wd:statement/Q1783179-dc5049b4-4cb6-5255-2931-8463efba0bcd |
| p:P4215 | wd:statement/Q1783179-2d8ef217-409e-0682-798f-082420ff1730 |
| p:P6104 | wd:statement/Q1783179-1D5C6B1D-2615-4255-9664-67AFC7D5480A |
| p:P6366 | wd:statement/Q1783179-927120E2-3E93-4347-A6B5-0A9FD1DF598D |
| p:P646 | wd:statement/Q1783179-F2BAACA1-D5DA-4F62-A1D8-19310CB38819 |
| p:P6781 | wd:statement/Q1783179-ad5a40e4-4d37-e6ae-5e9c-688441517ab0 |
| p:P7235 | wd:statement/Q1783179-423b90f3-46a6-2d2a-b3d7-af37aa7043a6 |
| p:P7554 | wd:statement/Q1783179-19ab5b38-425c-19ac-9232-50caecc5f147 |
| p:P8417 | wd:statement/Q1783179-7602f6e2-44b2-36b0-c170-7c34672d2cf3 |
| wd:statement/Q1783179-9fdd3a2d-413e-bc48-2513-4debba7939e3 | |
|
p:direct- |
<https:/ |
| wdt:P10283 | "C146561895" |
| 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"><msub><mi data-mjx-texclass="OP" mathvariant="normal">O</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">(</mo><mrow data-mjx-texclass="ORD"><mi>𝕂</mi></mrow><mo stretchy="false">)</mo><mo stretchy="false">=</mo><mo fence="false" stretchy="false">{</mo><mi>A</mi><mo stretchy="false">∈</mo><msup><mrow data-mjx-texclass="ORD"><mi>𝕂</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mi>n</mi><mo stretchy="false">×</mo><mi>n</mi></mrow></mrow></msup><mo stretchy="false">|</mo><msup><mi>A</mi><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mi>A</mi><mo stretchy="false">=</mo><mi>A</mi><msup><mi>A</mi><mrow data-mjx-texclass="ORD"><mi>T</mi></mrow></msup><mo stretchy="false">=</mo><msub><mi>I</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo fence="false" stretchy="false">}</mo></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P2579 | Lie theory |
| group theory | |
| wdt:P279 | simple Lie group |
| algebraic group | |
| compact Lie group | |
| compact space | |
| wdt:P2812 | "OrthogonalGroup" |
| wdt:P4215 | "orthogonal group" |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "146561895" |
| wdt:P646 | "/m/017gp1" |
| wdt:P6781 | "Definition:Orthogonal_Group" |
| wdt:P7235 | "<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>O</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P7554 | "Orthogonal_group" |
| wdt:P8417 | "Orthogonal_group" |
| "Orthogonal_group_for_a_symmetric_bilinear_form" |
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