Levi-Civita symbol
antisymmetric permutation object acting on tensors
| rdfs:label |
"Levi-Civita symbol"@en
|
|
skos:alt |
"Levi-Civitův pseudotenzor"@cs
"Permutační symbol"@cs
|
| schema:description |
"antisymmetric permutation object acting on tensors"@en
|
|
schema:date |
"2026-05-06T20:52:30+00:00"^^xsd:dateTime |
| schema:version | 2488296578 |
| wikibase:identifiers | 7 |
| wikibase:sitelinks | 29 |
| wikibase:statements | 16 |
| p:P10376 | wd:statement/Q623761-ddae1520-49e3-4089-6841-9f4f2a1d55dc |
| p:P11497 | wd:statement/Q623761-842510f7-46d2-0840-3b7f-6041c433bba4 |
| p:P1343 | wd:statement/Q623761-418922ae-40b3-4eba-3ea2-12377e6ab968 |
| p:P138 | wd:statement/q623761-28798B5A-AF28-467D-987D-F384F9D0B082 |
| p:P18 | wd:statement/Q623761-a824a1a9-4c94-520d-cc97-dadb9b0e2b38 |
| p:P1889 | wd:statement/Q623761-DF1522EB-424D-4310-9CAF-B819B8A283B4 |
| p:P2534 | wd:statement/Q623761-fad909b2-4ee4-a2db-e861-87b9d7aab56d |
| p:P2812 | wd:statement/Q623761-333bb3a6-4fa0-c382-b518-c200345b549f |
| p:P31 | wd:statement/Q623761-df422bdc-4bb6-f503-ff01-facd409d0b9c |
| p:P4215 | wd:statement/Q623761-788169E2-EA76-4738-A5AB-F4863D510877 |
| p:P5555 | wd:statement/Q623761-0b9858ee-4420-b148-616d-0eebd7ad422b |
| p:P6104 | wd:statement/Q623761-9C6B00B0-7482-4F6D-B9E0-FF3CF3F85EC3 |
| p:P6366 | wd:statement/Q623761-143C33F4-1190-4BCE-8529-E5A39FB92B9B |
| p:P646 | wd:statement/Q623761-ECD83565-BF6E-4E92-89D0-44497BC006BB |
| p:P7235 | wd:statement/Q623761-b72087de-43ac-9381-b024-67a508598e2f |
| p:P8885 | wd:statement/Q623761-6ca2f6d4-4c43-a83b-1349-38e826973d16 |
|
p:direct- |
<https:/ |
| wdt:P10376 | "mathematics/levi-civita-symbol" |
| wdt:P11497 | "1.6.E14" |
| wdt:P1343 | ISO 80000-2:2019 Quantities and units — Part 2: Mathematics |
| wdt:P138 | Tullio Levi-Civita |
| wdt:P18 |
<http:/ |
| wdt:P1889 | Levi-Civita connection |
| 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"><mrow data-mjx-texclass="ORD"><mtable columnalign="right left right left right left right left right left right left" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true" rowspacing="3pt"><mtr><mtd></mtd><mtd><msub><mi>ϵ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">…</mo><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow></mrow></msub><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">+</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mo stretchy="false">−</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo><mspace width="1em"></mspace><mi mathvariant="normal">∀</mi><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><mi>n</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd></mtd><mtd><mo fence="false" stretchy="false">{</mo><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo fence="false" stretchy="false">}</mo><mo stretchy="false">≠</mo><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><mi>n</mi><mo fence="false" stretchy="false">}</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><msub><mi>ϵ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow></mrow></msub><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>ϵ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>1</mn><mn>2</mn><mo stretchy="false">…</mo><mi>n</mi></mrow></mrow></msub><mo stretchy="false">=</mo><mo stretchy="false">+</mo><mn>1</mn></mtd></mtr><mtr><mtd></mtd><mtd><msub><mi>ϵ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">…</mo><mi>k</mi><mi>l</mi><mo stretchy="false">…</mo></mrow></mrow></msub><mo stretchy="false">=</mo><mo stretchy="false">−</mo><msub><mi>ϵ</mi><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">…</mo><mi>l</mi><mi>k</mi><mo stretchy="false">…</mo></mrow></mrow></msub></mtd></mtr></mtable></mrow></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"><mrow data-mjx-texclass="ORD"><mtable><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">ε</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo stretchy="false">…</mo><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow></mrow></msub><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mo stretchy="false">+</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>,</mo><mo stretchy="false">−</mo><mn>1</mn><mo fence="false" stretchy="false">}</mo><mspace width="1em"></mspace><mi mathvariant="normal">∀</mi><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo stretchy="false">∈</mo><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><mi>n</mi><mo fence="false" stretchy="false">}</mo></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><mo fence="false" stretchy="false">{</mo><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub><mo fence="false" stretchy="false">}</mo><mo stretchy="false">≠</mo><mo fence="false" stretchy="false">{</mo><mn>1</mn><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><mi>n</mi><mo fence="false" stretchy="false">}</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><mo>⟹</mo><mstyle scriptlevel="0"><mspace width="0.278em"></mspace></mstyle><msub><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">ε</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mn>1</mn></mrow></msub><mo>,</mo><mo stretchy="false">…</mo><mo>,</mo><msub><mi>i</mi><mrow data-mjx-texclass="ORD"><mi>n</mi></mrow></msub></mrow></mrow></msub><mo stretchy="false">=</mo><mn>0</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">ε</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mn>12</mn><mo stretchy="false">…</mo><mi>n</mi></mrow></mrow></msub><mo stretchy="false">=</mo><mo stretchy="false">+</mo><mn>1</mn></mtd></mtr><mtr><mtd class="mwe-math-columnalign-r"></mtd><mtd class="mwe-math-columnalign-l"><msub><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">ε</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">…</mo><mi>k</mi><mi>l</mi><mo stretchy="false">…</mo></mrow></mrow></msub><mo stretchy="false">=</mo><mo stretchy="false">−</mo><msub><mrow data-mjx-texclass="ORD"><mi mathvariant="normal">ε</mi></mrow><mrow data-mjx-texclass="ORD"><mrow data-mjx-texclass="ORD"><mo stretchy="false">…</mo><mi>l</mi><mi>k</mi><mo stretchy="false">…</mo></mrow></mrow></msub></mtd></mtr></mtable></mrow></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML | |
| wdt:P2812 | "PermutationSymbol" |
| wdt:P31 | function |
| wdt:P4215 | "Levi-Civita symbol" |
| wdt:P5555 |
<http:/ |
| wdt:P6104 | WikiProject Mathematics |
| wdt:P6366 | "42164691" |
| wdt:P646 | "/m/01bvm8" |
| 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>n</mi></mstyle></mrow></math>"^^http://www.w3.org/1998/Math/MathML |
| wdt:P8885 | "레비치비타 기호" |
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